It's actually faster than that, gaming and otherwise, 8700K is practically on the heels of Ryzen 7 1800X.
Clock for clock, the i7-8700K delivers 2.5 times the performance of Sandy Bridge's finest four-core avatar in our productivity index.
They assume i7-8700K is 2.5 times faster than i7-2600K, but that's just the bias of their weighting formula.
It's certainly not that faster "clock-for-clock", i.e. clocked on the same frequency - the last three major generations of Intel processors (i.e. Sandy/Ivy Bridge, Haswell/Broadwell, and Skylake/Kaby Lake/Coffee Lake) have very similar IPC , and real-world performance gains come from increased clocks and cache memory, made possible by process node improvements.
So performance gain can be roughly estimated using turbo clocks and number of cores: for Core i5-2500K and Core i7-8700K, that would be (4.3*6)/(3.3*4) = 1.9, or
90% faster - assuming workloads that scale very efficiently with many-cores, such as video encoding.
If you count in HyperThreading in Corei7, that could give you additional 20-30% over Core i5 in ideal conditions.
So in the end, 8700K would be about 2x (or 100%) faster, but not by a wide margin, in many-core workloads. For single-threaded workloads, it should be about 30% faster (4.7/3.7=1.3).