World Series has always been on (also league championships), 1 year had all the mets fans for jersey week watching which was always colorful.
With NFL most of the times they have the games on in the bar as well as your TV in your room. I would say the Wonder and Magic are better set up for getting almost all the NFL or College games going that they can find (more TVs) The Fantasy Bar is so small and less TV's and sometimes they cannot get what people ask for (there specific game). Never been on the Dream for Football Season but guessing alot like the Fantasy.
As for Monday night and Sunday Night Football I always remember those being on.
Also talk to your bartenders, they have the daily schedule that the ships entertainment person puts out on what there supposed to put on and when. This helps if you need to "Lobby" the people in charge to possibly find your game. Some bartenders know how to get things done and get your game on for you, others are clueless and wont be of any help (you figure this out right away).
I watched the Mets fans get all of the games on the TVs one night in the Fantasy bar, they had the Monday Night Game on all but 2 of the TV's and "Lobbying" started and next thing you know the games was on all of the TVs (except one).
I agree Disney is ESPN/ABC but on the water its international everything and ESPN International is much different in what they show vs USA ESPN from what I have seen and noticed travelling.
Hope this helps