Jose Mourinho's first match at Chelsea was quaintly local and low-key: a 1-1 draw at Oxford United back in July 2004, featuring the likes of Celestine Babayaro, Steven Watt and Craig Rocastle. Then came a pre-season tour taking in Seattle, Pittsburgh and Philadelphia. Chelsea strutted across the US, building their brand and flinging banknotes. The club spent £50m on Didier Drogba, Ricardo Carvalho and Tiago in the space of a week.

At the dawn of Mourinho's second coming, Chelsea have returned to America. They faced one of his former teams, Internazionale, in Indianapolis on Wednesday night, dominating and winning 2-0 with first-half goals from Oscar and Eden Hazard, from a penalty, in front of 41,983 at Lucas Oil Stadium.

Chelsea are now more familiar with the US than Oxfordshire: this is their eighth visit since 2004. It is only 69 days since they faced Manchester City at Yankee Stadium as part of a post-season tour. And it is only 10 months until the 2014 World Cup finals, with the former England manager, Fabio Capello, once again blaming tiredness for England's grim time in South Africa last time out.

Chelsea are in the middle of a stretch of seven matches in seven cities across two continents in 24 days: Bangkok, Kuala Lumpur, Jakarta, Indianapolis, New York, Miami, Washington. They arrive back in England a week before they start their Barclays Premier League campaign, against Hull City on 18 August.

Chelsea are one of eight clubs taking part in the Guinness International Champions Cup, which is among the biggest, most sprawling and ambitious pre-season tournaments to date. Aiming to put the glory into "glorified friendly", with a trophy, a knockout system of sorts and a defined path to the final, it is designed to be a more formal and prestigious successor to the nebulous World Football Challenge (WFC), which was held in the US and Canada between 2009 and 2012.

The Champions Cup includes the best of MLS, the Los Angeles Galaxy, and some of Europe's elite teams, with Everton (champions of England as recently as 1987) acting as the control group in this particular experiment. Bizarrely, the opening match was in Spain – Milan beat Valencia 2-1 last Saturday at the Mestalla. Equally strangely, two baseball stadiums are host venues, though both Busch and Yankee Stadiums attracted excellent crowds back in May, for Chelsea and City.

Everton beat Juventus 6-5 on penalties after a 1-1 draw on Wednesday, in front of 22,208 at AT&T Park, the home of the San Francisco Giants. The same night, Major League Soccer hosted its All-Star Game in Kansas City, before a sell-out crowd of 21,175. So the domestic league's second-highest-profile match of the season had to compete for attention with a tricked-out exhibition game between foreign clubs in a ballpark. And with baseball-related publicity stunts involving Cristiano Ronaldo.

The Galaxy are like travellers straddling the parallel universes of MLS and the Champions Cup. Bruce Arena's team did not even play in their own state in the first round. They met Real Madrid in a suburb of Phoenix, Arizona, on Wednesday night – the fourth summer fixture between the clubs in four years. Real outclassed the Galaxy 3-1, in front of 38,922. On Saturday, both teams head to Dodger Stadium, which has never before hosted football.

Despite all the league's shiny new soccer-specific venues, no MLS stadiums are being used – they are mostly too small. Arena described the scheduling as "odd". The Europe-focused Fox Soccer is showing 11 of the 12 matches live, with another on Fox Sports – a last hurrah, since the channel lost its Premier League rights to NBC Sports and will soon close, with its content shifting to the incoming Fox Sports 1. The plan is for the new channel to televise next year's tournament.

Friendly rivalries – a history

Tours are innocuous moneyspinners and bonding exercises for overseas clubs but in North America they are touchstones for key questions. Who controls the sport in the US? Who profits? Does the annual arrival of glamorous and superior foreign teams in the middle of its season help or hurt MLS?

More than a decade ago, Charlie Stillitano, a former general manager of the New York/New Jersey Metrostars, spied an opportunity to woo European clubs to the US to play friendlies in the summer on an organised basis. MLS was young and struggling but memories of the attendances and interest at the 1994 World Cup finals were still fresh. The US offers excellent training facilities, large crowds for matches against high-calibre opponents and relative anonymity for the players, who can step out of their hotels without being mobbed, unlike in Asia. And imagine the potential profits and business opportunities for clubs in a rich and untapped nation of more than 300 million people. Increasingly, through ownership or sponsorship, some of America's most powerful corporations and individuals have strong financial incentives for European clubs to prosper.

Stillitano launched ChampionsWorld, which in 2003 persuaded the dream draw, Manchester United, to cross the Atlantic to play very popular friendlies against Celtic, Club America, Barcelona and Juventus. United and Celtic returned the following year and were joined by the likes of Liverpool, Milan, Bayern Munich and Chelsea. It was a spectacular roster, but ChampionsWorld was in debt and costs were high – top clubs do not play for free. Hiring Manchester United reportedly costs up to $2m per match. And the organisers had to pay the US Soccer Federation more than $3m for the right to stage the games.

In 2005, ChampionsWorld filed for bankruptcy; in 2006, its creditors sued MLS and the US Soccer Federation, alleging that the two authorities had conspired to make life impossible because they feared that private promoters staging international matches were undermining MLS. The league has its own promotions arm, Soccer United Marketing (SUM), which has organised exhibition games in recent years.

Legal arguments ensued as to whether under US law and Fifa rules, the Federation had the right to control all professional matches under its jurisdiction, even if they were organised privately and involved foreign teams. Last August, a US district judge ruled in favour of US Soccer in the antitrust lawsuit but said that it only had authority over Olympic-related events according to US law. Not important, said US Soccer, as its lawyers did whatever the legal equivalent of a goal celebration is: our stranglehold derives from powers given to us by Fifa.

Stillitano rebounded to run the WFC with a colleague, Jon Sheiman – partnering with SUM/MLS and Creative Artists Agency, the massive Hollywood talent agency. Last year Sheiman and Stillitano agreed to join a new sports and entertainment company called RSE Ventures, which has lots of clever ideas about how to part fans from their cash.

It acquired the rights to the WFC and formed a New York-based, spellcheck-defying division called Relevent Sports. Last year's WFC featured four MLS teams and nine fixtures and was heavily promoted on the official MLS website. There were no matches within three days either side of the All-Star Game. This year, though, MLS has no involvement in the Champions Cup beyond the Galaxy's participation and its website has largely ignored it.

The showpiece games are in South Florida's ageing Sun Life Stadium, home of the Miami Dolphins. RSE's joint-founder, the real-estate billionaire Stephen Ross, owns the Dolphins and the stadium. Since Miami is trying to win a new MLS franchise that would most likely have David Beckham as a figurehead, packed stands for this orgy of international star power would help bolster its claim to be a football hotbed. The Miami Herald reported this week that the games on 6 and 7 August are expected to sell out. Two-day, four-game passes cost from a reasonable $72.20 to a ridiculous $1,126.90, through Ticketmaster.

Logically enough, SI.com's Grant Wahl reported earlier this year that Ross is a contender to own any future Miami club. Perhaps MLS and the International Champions Cup will soon have something in common, beyond the token participation of the Galaxy.

Champions Cup – the teams

Milan
Manager: Massimiliano Allegri (since 2010)
Key ins: Cristian Zapata (Villarreal), Andrea Poli (Sampdoria), Jherson Vergara (Quindio)
Key outs: Massimo Ambrosini (Fiorentina), Mathieu Flamini (released)
Last season: 3rd, Serie A

Chelsea
Manager: Jose Mourinho (since 2013)
Key ins: Cristian Cuevas (O'Higgins), Andre Schurrle (Leverkusen), Mark Schwarzer (unattached), Marco van Ginkel (Vitesse Arnhem)
Key outs: Yossi Benayoun (released), Paulo Ferreira (retired), Florent Malouda (released)
Last season: 3rd, Premier League

Everton
Manager: Roberto Martinez (since 2013)
Key ins: Antolin Alcaraz (free agent), Gerard Deulofeu (Barcelona, loan), Arouna Kone (Wigan), Joel Robles (Wigan)
Key outs: Thomas Hitzlsperger (released), Phil Neville (retired), Jan Mucha (released)
Last season: 6th, Premier League

Internazionale
Manager: Walter Mazzarri (since 2013)
Key ins: Ishak Belfodil (Parma), Alessandro Capello (Bologna), Mauro Icardi (Sampdoria), Hugo Campagnaro (Napoli)
Key outs: Antonio Cassano (Parma), Giulio Donati (Leverkusen), Luca Caldirola (Bremen)
Last season: 9th, Serie A

Juventus
Manager:
Antonio Conte (since 2011)
Key ins: Carlos Tevez (Man City), Fernando Llorente (Athletic Bilbao), Angelo Ogbonna (Torino), Federico Peluso (Atalanta)
Key outs: Vincenzo Iaquinta (released), Emanuele Giaccherini (Sunderland), Felipe Melo (Galatasaray)
Last season: Champions, Serie A

LA Galaxy
Manager:
Bruce Arena (since 2008)
Key ins: Carlo Cudicini (Tottenham), Robbie Rogers (unattached), Pablo Mastroeni (Colorado), Laurent Courtois (unattached)
Key outs: David Beckham (released), Christian Wilhelmsson (Baniyas), Mike Magee (Chicago)
Last season: Champions, MLS

Real Madrid
Manager:
Carlo Ancelotti (since 2013)
Key ins: Asier Illarramendi (Real Sociedad), Isco (Malaga), Daniel Carvajal (Leverkusen), Casemiro (Sao Paolo)
Key outs: Gonzalo Higuain (Napoli), Raul Albiol (Napoli), Jose Maria Callejon (Napoli), Ricardo Carvalho (Monaco)
Last season: 2nd, La Liga

Valencia
Manager:
Miroslav Djukic (since 2013)
Key ins: Michel (Levante), Oriol Romeu (Chelsea, loan), Javi Fuego (Rayo Vallecano)
Key outs: Fernando Gago (Boca Juniors), Nelson Valdez (Al Jazira), Alberto Costa (Spartak Moscow), Roberto Soldado (Tottenham, pending medical)
Last season: 5th, La Liga

Results

Milan 2-1 Valencia
Juventus 1-1 Everton (Everton win 6-5 on penalties)
Chelsea 2-0 Internazionale
Real Madrid 3-1 LA Galaxy

Fixtures (all times ET)

Saturday: Juventus v LA Galaxy (8pm, Dodger Stadium, Los Angeles); Everton v Real Madrid (10.30pm, Dodger Stadium).
Sunday: Valencia v Internazionale (4pm, MetLife Stadium, New York/New Jersey); Milan v Chelsea (6.30pm, MetLife Stadium).
6-7 August: Championship game and three play-offs, Sun Life Stadium, Miami.