Being a good computer programmer would put your son in demand. Specializing in computer gaming still gives the programming knowledge, but can also require significant mathematical knowledge. Computer science + math should give him lots of career options. The programmers I know are doing quite well. However, I will say that lots of companies will hire only candidates with 2-3+ years experience, and your son may have to intern or work for a low salary for a few years to get that experience. After that, however, he should do well because good, experienced programmers are in high demand, at least in my area.
For reference, my husband (who was home schooled) worked a paid internship until he was 19, when he got a full time programming position at a low, but livable salary. He was even able to pay my college tuition so I could avoid loans. We did eat a bit of ramen though. He was with that company about a year before searching for a new job, landing one with about an 85% raise. His salary has continued to climb (not 85% a year, of course) since then, and we are now quite comfortable. He just needed a couple of years experience under his belt, and has absolutely no problem finding a new job (with higher pay) when he is not happy with one. He is also really, really good at what he does, and attends nearby professional conferences for networking, so that he even has standing job offers in case he needs them.