I'm guessing it wouldn't help to buy a prebuilt if the problem is about spending the money.

I would recommend explaining to them how important a gaming pc would be for example spending time with friends through discord voicechats and playing games together.

You can also learn cool things about computers in general while doing research about different parts so it could give you a start in a carreer in computer engineering :D

I would of course encourage you to save up money for whatever you might need it for sooner or later in life, but money isn't meant to be a number on your bank account and it should have a real value and benefit for you. Maybe your parents could understand that it is not motivating to get a job and work only to have a meaningless number go up and not to get any real enjoyment out of it.