I'm like you, Flame - just not 100% convinced that my son has AS, but he certainly has a lot of overlaps in his behaviour with AS children. Mine (age 4) loves letters, numbers and singing (connected to the counting, as he sings his songs in order as per the CD player and knows what number each song represents) - he would happily count, do sums and times tables, watch the CD player count up to 50 as it plays his favourite nursery rhymes, etc, all day - in between playing board games like snakes and ladders which involve lots of counting. However, that doesn't mean that be NEVER plays role-play type games (eg we have a doctors' kit he pretends to use occasionally, he's been known to make us pretend food and he sometimes plays Bob the Builder games with his brother, where they pretend to saw up all our furniture. He also knows how to play appropriately with toy garages, etc, and makes up funny stories, it's just that these really aren't his first choice of activities).
He never draws pictures, but will draw letters and numbers and can read fluently but prefers to be read to. However, he has a great imagination, is really thoughtful, loving and cute, is good at sharing, plays just like a NT child with his brother, and will let me bully him into trying out other activities from time to time. He is very eager to please adults, so will do activities he dislikes at school if the teachers ask him to. He still doesn't see the point of friends - he's got his brother, parents and the teachers and doesn't see why he needs to play with anyone else. However, he isn't actually keen on playing alone - he likes us all to be around, involved in his counting (yawn, yawn).
Perhaps I'll get away with telling everyone he's just gifted at maths and a bit obsessional and that's why he's a bit unusual!!!!! My husband was a little bit unusual when he was little, too (not quite so marked, it has to be said, and without the additional problems with hypotonia and hypermobility) and he is most definitely NT, now (if there really is such a thing - I think we're all weird in one way or another, it just depends how good we are at hiding it).