Gaming generally requires faster cores, and doesn't utilize more than 2 in most cases (4 in some instances).
The 4690K is 100% a worthwhile upgrade from your FX6300......but there will be a significant cost involved.
1. The CPU itself
2. A new motherboard - needless to say, your AMD board will not support an Intel chip
3. If you have an OEM version of Windows, you'll need to buy a new OS too.
That puts your right around a $400 investment, so you'd need to consider whether you can live with the FPS you have, or if you're prepared to spend the required amount for that specific upgrade.
There are other options available to you though. An i3 with Hyper-threading would likely serve you better than the FX6300. Haswell i3's are priced pretty much the same as Skylake i3's, so Skylake would make the most sense. Skylake i3 + Z170 board + OS for around $300, but you should then explore DDR4 also.
There are other options on the AM3+ socket, but those tend to generate more heat & really, I wouldn't be comfortable recommending you invest more in an AMD socket.