You can convince them by getting a job and buying your own gaming PC.

Tell them off by saying its your cash, and account.
If not, sue them old fashioned raisin people.

For anyone wanting to see how this turned out, here is what happened. So as I said whenever I bring up the subject they avoided it like the plague. But 2 weeks ago my family and I got stuck at a restaurant because they were having problems with their credit card machine. Because I had a captive audience I was able to talk about the subject, they then brought up their problems with it (instead of walking away), and I addressed/ disproved all of them.

ThatSniperGuy wrote For anyone wanting to see how this turned out, here is what happened. So as I said whenever I bring up the subject they avoided it like the plague. But 2 weeks ago my family and I got stuck at a restaurant because they were having problems with their credit card machine. Because I had a captive audience I was able to talk about the subject, they then brought up their problems with it (instead of walking away), and I addressed/ disproved all of them.

I love the fact you beat them in a debate about how good technology is, because you were stuck at a restaurant while technology was failing on them.. lel, the irony. To be honest, if it was me, I'd have said from the start "it's my money and I dictate what I spend my money on, not you. kthxgbye"

ask them to buy it for birthday!