Crysis 3, and BF4 currently use 7-8 threads in this generation, there are many already using 4 threads. Things are only going to get more and more threaded as time goes on.
So, to answer your question, yes...there will likely be many games in the next few years that won't hit numbers beyond 60 FPS without 6+ core CPUs.
As a game developer, I can tell you this much:
Any game developed on Frostbite 3, CryEngine 3.5 or Unreal 4 will use at minimum 4 cores, and likely 5-6+ if it's demanding at all.
For example, MechWarrior: Online will tap 4-5 cores on my 8350 up to 70-80% when I play on the weekends. That's an online game too...but it's built on CE 3.5 and it's a very beautiful game.