It seems like since WWI, many aspects of culture have been dominated by the US, including music, film, literature, television, advertising, and even the Internet. Dissidents call this imperialism. makes sense.
Why is it then, that "American" sports never became global? American football barely has a presence outside North America, and baseball only has a dozen or so prominent nations. What made American sports so unappealing to other nations?
I think you're drastically underestimating how popular American sports are abroad.
Basketball is massive in China and Taiwan, so much so that the American NBA regularly does exhibition games there. Baseball is ridiculously huge in Korea and Japan and has been for decades. Pool (the kind from America) is also incredibly popular in Asia and regularly broadcast on tv, though I don't know if you're just thinking of team sports.
You could make the case that American football didn't spread well, but no one's football really spread well except soccer. You don't really see people playing Gaelic football on a large scale, though there are private groups that do organise games. However even American football gets played in Asia on a small scale, e.g. in Taiwan and by Taiwanese people, not Americans living in Taiwan.
I would highlight one difference between most the examples of culture the OP listed that have spread and sport: they were transmittable internationally prior to the spread of television and the internet.
Film reels, vinyl records, books, etc. could be sent overseas for international consumption much easier than sport. In the case of music, the albums could be used to generate interest prior to an international tour, should an artist opt to do so. A record or film produced in the US could be experienced by an American and an international consumer in almost the same way.
Sport is typically something one experiences either by playing the sport (which requires knowledge of the rules and set-up, plus any necessary equipment) or by watching (difficult prior to television, should the sport not already be widely spread in the area). Radio broadcast was possible, but garnering an audience when few people in the area are familiar with the sport is unlikely. Gaining new fans for the sport would likely be challenging - without understanding the rules of a game, the play-by-plays would likely be incomprehensible. Teams traveling would likely have difficulty filling a stadium, however.
Soccer/association fooball had an advantage over American sports in spread: The British and Europeans colonized, and they were therefore able to spread their cultural heritage, including sport, through contact. Oftentimes sport was purposely used as a "civilizing" force for native populations and lower classes, as it was considered to instill proper values. American sports have a stronger foothold in the areas the US has been involved in - Asia, the Caribbean, and South America.
J. A. Mangan has works on sport and imperialism that may be of interest