Sorry to disagree, but there sorta is, and has been. The recommended requirements for almost all games a few years back was 3.2GHz. This often played out as an above average amd or average Intel cpu.
Once cpus really started getting ahead of that, stock speeds of 3.4GHz or better, quad core cpus being now mainstream, then that was kind of forgotten about, and changed to specific cpus being the minimum.
But in the gaming world, fps (frames per second) is all about the cpu. The stronger the cpu, the faster it is, the more threads it has are all variables that apply to different games. SWBF2 is a heavily threaded game, 8 threads is almost a must for best fps. CSGO is 2 threads, fps count relies heavily on clock speeds and the cpus IPC (instructions per clock). The stronger the cpu, the higher the fps.
So for CSGO, anything fast with at least 2 threads will get you in fps well above even the fastest refresh monitors, but that same cpu would tank in SWBF2.
What you should be looking at is a cpu that has higher clock speeds (or ability to OC to get higher), has good IPC (anything in the last 2 generations of either Intel or AMD) and enough threads to cover the most demanding games. The best 2 cpus for the price are the Ryzen 2700x and Intel i7-9700k. Currently. Ryzen (Zen2) 3000 series cpus will supposedly go public as of July 7 and reportedly will match Intel IPC or beat it. That would make the $199 Ryzen 3600 a serious contender for best all around cpu as Intel has nothing even close in that price range, at that IPC, with 12 threads.
And it'll overclock, and it'll work well on the better B450 motherboards, which aren't as expensive as the Intel Z390 needed for the 9700k.