I don't know of any games that currently use MORE than 8 cores, however, if you are a heavy multitasker and like to stream, record, encode, browse with many tabs, play music, etc., any or all of the above, simultaneously, WHILE gaming, or even just a couple of different processes at the same time, then you could easily see some benefit from 8 or more cores.
If you don't do any heavy multitasking, then an 8 core CPU with an additional 8 hyperthreads is plenty for pretty much anything currently out there that is not strictly scientific or advanced video encoding. Maybe also some professional CAD and graphics applications.
I'd say you'd be perfectly fine with a 3000 series 8 core CPU for gaming, regardless of what graphics card you choose to go with.