Most obvious difference between NT's and aspies from a social perspective is that NT's seem to play "the game" to get to know other people better, whereas aspies get caught up in the actual "game".
There's pretty much always a game, whether it's explicit or implicit, if you're at a bar maybe it's dancing, if you're playing monopoly, cards, soccer, at work it's working, when you go shopping it's finding a good deal. There's always a "game".
For example, NTs poker players range from serious and competitive to laid back and talkative. But they are all there either to make friends or measure up against someone else, it's all about the individuals they are playing with, the cards and chips are merely a facilitator, a kind of social lubricant.
Aspies play Poker and their reactions go from an intense focus on the poker chips and the arrangement of the different symbols on the cards to those that just want to put a bullet in their heads out of boredom. Noone is really caring about the people and generally winning isn't number 1 on the priority list either, although not losing many times is because of the sheer fascination. When I play poker I'm so focused on the flow of the actual game I forget that the people I'm playing with even exist.
Coincidentally, I think a lot of aspies approach socialization as just another task, another "game" to be played, which is weird for NT's who see this as a totally separate and spontaneous thing that arises from the game.
I feel like that's a pretty clever way to put it.