When you say GPU, does Intel HD graphics count? I know it is an integrated one, and doesn't compare to a geforce, but every machine i have only has Intel HD.

(I guess is too soon to say, so I'll speculate.)

My guess is that if Casey started writing the accelerated renderer today, he would use OpenGL. If he decided to go with OpenGL 3.X, you would need a card produced after 2011 in order to to compile and execute that renderer. Performance, however, would depend very much on the exact model of your card.

But of course, Casey has already stated that he will resort to Vulkan if it's ready by the time he starts writing the accelerated renderer. I don't know which intel HD cards will get Vulkan support. Here's some people people guessing at reddit.