Have been reading some game programming (very little) the last couple of days checking how it is done. What strikes me is that how little the performance of the game depends on the processor. If you can run the game on 640x480 then the processor is ok. How high (resolution) you can go depends on the video card.
There seems to be very few (if any) settings in games that will add work for the processor that are resolution dependent. AI and physics, detail etc will probably add work for it, haven’t read about that. But it should be the same for all resolutions.

Games don’t seem to use take advantage of higher resolutions for increasing the game experience for the player.

If the game is using threads then one single core processor should degrade performance but apart from that it’s the video card that decides game performance. Faster processors will of course increase FPS on low res but you will not go below min FPS on 640x480 because the processor isn’t enough on higher resolutions. If you go lower then it depends on the video card or something else, not the processor.

All this talk about what type of processor you need for gaming seems to just be fictional.