Magnus,
With video output from a computer, the action is mainly in the video card and while you can pay a fortune for high end video cards, it would seem that the only differences are in test software that tries to determine frame rates on a game by game basis.
If you are into very high end gaming you may find some advantage in high frequency monitors that are large like 32 inch or bigger but you also need some high end grunt that is fast enough in the CPU department, late model Intel or AMD CPUs which can sustain high clock rates if they have enough cooling.
My main dev box is 5 years old and it still has its 4 gig Nvidia 960 video card as it has done everything I have ever pointed at it. The later boxes I have built have 8 gig Radeon RX 580 video cards which perform well.
CPU wise, I have two 5820k i7's and two Xeon E5-2690v3,s but its mainly because I need to be able to thrash the guts out of them processing video where industrial style processing and appropriate cooling solutions are the main advantage.
Gaming computers tend to have fewer cores but cores that run faster, some up near 5 gig and the results depend very much on the way the games were coded.