Your I7-2600K is still very good for gaming.
I see that because of your H61 motherboard, you are running at stock speeds.
Passmark shows your cpu rating as 8478 and 1943 for single threaded performance.
I suspect your actual rating is lower because most users of 2600K@3.4 will have been overclocked.
The I3-6100@3.7 rating is 5480 and the single thread rating is 2106. A nice boost in single threaded games.
But, it only has 4 threads.
The better performer will be the I7-6700 option with 8 threads and a rating of 10036/2158.
But, of course, the cost is greater.
I don't know that I would be thrilled with either option.
What kinds of games do you play?
Some games are graphics limited like fast action shooters.
Others are cpu core...