It’s entirely dependant on the game and what experience you want him to have. What sort of games does he play? The latest ones? Most of them now need a monster PC to play well on.
If he’s happier playing last years games then chances are you can get away with less, but unfortunately it’s not an exact science.
As a rule of thumb though, the graphics card is your main driver. To do the gubbins nowadays, the graphics card will typically cost as much as, or more than the rest of the PC.
And I’m sorry to say, that even a half decent PC is going to cost a fair bit more than an XBOX360 (for example).
A reasonable gaming PC that will play modern games at a sensible lick will cost you around 300-500 quid, easy, and I’d say that’s minimum spec.
For example, this is what I’d say is a mid level gaming PC, but it doesn’t come with a screen, keyboard or mouse, add another hundred on at least for those.
http://www.custompc.ie/intel-gaming-pc—level-2-20050-p.aspp
I built up my current PC (which is about the same spec as the above) for about 150 quid but I used the old screen, hard drives and case.