I believe NTs can obsess but they do it emotionally. So for example the difference between an aspie and an NT being obsessed with (Australian) football would be like this-
Aspie- focuses on one team. Learns the names of all the players, past and present for the last 10 years. Remembers all the games they played, each round, against who, if it was a win or loss, the scores and margin. Remembers coaches over the years, when the team was first established. Historical win/loss records for each playing ground. Historical win/loss records against each other team. Couldn't care less about watching them live, rather watches taped games over and over and over to learn every move made for every game, learning the commentator commentary by heart in the process. Their team winning a grand final is another stat, and another game to watch taped over and over.
NT- focuses on one team, usually one in the same city. Absolutely must go to that teams games if they are playing that week at the NTs city. God forbid you try to stop them going to games if their team gets into the finals. When at a game or watching one has a completely one eyed view of the umpiring, in which penalties against their team are always wrong. Has to watch the game live but is dis-inclined to ever watch a game a second time unless its a grand final their team won. Often yells abuse at the other team when they play good and cheers loudly, yelling when their team does good. May learn historical win/loss records at each stadium. Always bets on their team to win, always. Takes special care to play along with any team rivalries their team may have. Mostly would only know their teams current players by name. If their team wins a grand final it is an awesome excuse for a party so they can brag to all their friends about how their team won the grand final.
I guess aspies have interests, rather than being passionate about them they have an intense drive to learn more. NTs get passionately involved, or emotionally involved.
Of course this is a guess, generalisation and stereotyping, it could be wrong but generally i think this is true

My NT nephew is in the middle of this. I don't think he watches a game over and over, but he can quote baseball statistics for all teams as far back as he can go. He has an incredible memory. He can look at any baseball team and tell you who is batting next and what their records are. I wouldn't call him obsessed, but he does have a strong interest in sports and he remembers a lot of stats and details. He does favor his local teams, but also favors others too from time to time, and certain people. He doesn't always bet on "his" team however. He bets the odds.
I think anyone can be obsessed, but I see what this post is saying and I tend to loosly agree. I see the interest in baseball with my nephew, but I don't see the "intense" drive to learn more. I think that's a good point, intense being the operative word. That's the impression I get.