Even though you have the S variant (no OCing, lower power draw etc), it's still a very, very capable CPU.
Some people upgrade to simply say they have the 'latest and greatest'. Totally unnecessary from a 3770S currently.
As for "how long" for 60FPS at 1080p, that'll mostly depend on the GPU it's paired with and the settings
A 3770S would pair well with even something like a GTX1070 today (at 1080p, max settings >60FPS)
I'd guesstimate it's got a couple more, strong years left in it.