He sounds like he is very bright, but as for "gifted", or how bright he is exactly, I think it depends on how much time you are spending teaching him. For instance does he skip count because you have spent a lot of time rehearsing, or does he truly understand the concept? Does he know shapes like trapezoids because you talk about it a lot, or does he pick it up with seemingly no effort?
Some of the things on your list are actually red flags for disorders like autism or Asperger's, for instance not playing with other kids (kids that age do a lot of parallel play rather than interacting, but he should be interested in what other kids are doing and want to be near them), the perfectionism (needing things to be in a certain order or lined up), sensory issues, not playing with toys, and being extremely interested in the alphabet rather than normal toys. At that age he should be doing pretend play. For instance if you give him a play phone will he put it up to his ear and pretend to talk, even though he knows it's not a real phone? Does he play with toy cars or trains and pretend they are real? DS would move his trains around his tracks while yelling "choo choo" at that age, and he would make his trains talk to each other. I'm not trying to diagnose him with anything, I was just concerned by a few of your bullet points.
