Good question - I'm not entirely sure. Without the cultural dominance of the Anglosphere after WWII, it is likely we'll see more local and regional styles, fewer big international hulabaloos. Of course we would still have the Olypmics and international racing events, but these are not going to turn into things that dominate international news the eay the World cup and Summer Olympics do today. More like Paris-Dakar or Wimbledon - big and profitable for sure, but ignorable and not politically significant.
Within postwar Germany, sport is going to be a very important social phenomenon. First, because it's the twentieth century and people believe in it. Secondly, because it is a form of entertainment that can be provided to the people relatively inexpensively from local resources (building soccer pitches and cross-country trails looks good and creates jobs). Thirdly, because it lends itself so well to collective organisation. For decades to come, sports will be an intensely political thing. What sports you do and who you do it with will locate you in the political spectrum. Socialist organisations will sponsor sporting activities while bourgeois foundations put money into lavishly equipped facilities to lure proletarian youths away from 'dangerous influences'. For a long time, championships (at the member state level) are going to play out among political foes. If VfL Germania Kiel meets Rot Sport Altona in the finals, there will be blood in the streets. When Ha Koah Berlin play 1. FC München, there will be radios on in synagogues from Flensburg to Berchtesgaden.
Now, I envision German sports culture to be more club-oriented and local than the modern Bundesliga. Sponsorship will mostly be from individuals and businesses that identify with 'their boys', there will be fewer superlucrative advertising deals and, as a result, players will move less often and be bid for less aggressively. By the time TV comes aropund, being an athlete can be lucrative, but it isn't a path to instant riches and celebrity.
Given the clubs will not be able to agree on championship formats for a long time, I expect those will ultimately be enforced in the context of some QUANGO-ish association with mandatory membership. That means TV rights will automatically go to public broadcasters. No multimilion-mark contracts, and clubs will have to rely more on merchandise and ticket sales for income.
Beyond soccer, there will be other popular sports in the media. Some of them will be the old gentlemenly entertainments. The nobility have a stronger presence on Germany's media, which means more coverage of equestrian sports, rowing, fencing and lawn tennis. Then there will be the "equalising" mass sports: athletics, handball, boxing, wrestling and increasingly swimming. The military has a strong presence here, with competitors detailed from their regiments to train and attend championship events on full pay as a matter of national pride.
Eventually I am sure there will be international championships in many sports as national federations get their act together, but a lot of the early limelight will be stolen by the Olympics and there will be wrinkles to iron out between different national rules. Some sports will remain mainly national or regional media phenomena - baseball in the United States, cricket in the Empire, savate in the Francophonie, sabre fencing in Germany.
