Those sports are popular in America, but have very little following worldwide. I wasn't sure whether you took that into account when you say "popular today".

America is therefore the outlier on this one in not having football ("soccer"), cricket or rugby as its major sports.

As to why America appears unique in its sports choices, I honestly don't know! If I were to speculate, it would be to do with colonisation. Games such as cricket are spread over the British empire, for example, as is rugby. America large enough to be a market for its own sporting culture, but became independent before the establishment of the other worldwide sports.

It's striking to me that the main American sports all have a similar-ish equivalent in world wide sports, suggesting the core components of the games may have had more universal origins before rules were formalised. (eg bat and ball games as a team = cricket and baseball; getting an egg shaped ball to a goal = American football / Rugby; throw a ball in a high hoop as a team = basketball / netball)