I was in a pretty similar situation not too long ago, albeit more abusive, bit with a similar feeling of being treated below my age/intelligence.
It's absolutely not your fault that moving around a lot has impacted your pool of friends (or lack thereof), but the way a lot of adults are going to view it is that you're a kid, you've got it a lot better than they do as adults with responsibilities (which includes taking care of you). They probably can't remember their own teenage years with much accuracy, because you probably get the feeling they expect you to have the kind of social life straight out of the movies, right?
As far as they know, you're a kidnerd shitkid who sits in the basement clickity clacking to a bunch of colors on the screen, rejecting human interaction and responsibility. The best thing you could do would be to do things for yourself that exemplify your ability to do things for yourself. Acting like an adult is how you get treated like an adult. Prepare a resume, look for jobs you could take public transit to if that is an option, manage your time so that you aren't always on the computer.
Right now I am up in Canada with my fiance and his family until August. At home, all I do is draw. Up here, I balance my computer time with family time, and I often clean up after my fiance and his family when they are at work or school. I even fall back to my oldest-loved hobby: reading. I try to contribute while also using my time on the computer to do more than entertain myself. Through my art, I try to also be productive. The last thing I want to do is present myself as a complete computer-addicted shut-in to these people. The thing is, I genuinely like these people. I know it's harder when you feel like you and your own family just don't connect. But that's when you have to remember that you are nearly a man grown, and that you aren't really doing these things for anybody but yourself. It directly benefits you and only you to seek employment, volunteer work, a hobby.
Find something relevant to your interests, like computer programming.