As profoundnoah said, for gaming, the highest-end CPU won't matter much if the graphics card is holding it back. An 8700K will offer a bit faster per-core performance compared to a 2600X or overclocked 2600, but that's not going to really make any significant difference unless they are paired with a high-end graphics card that can reach high enough frame rates to push the CPU to its limits.
And you won't be overclocking either of those i7s to any substantial degree unless you get a high-end cooler for them. For gaming, a faster graphics card will generally be more important than a faster CPU. And even for streaming, an overclocked 2600 should perform pretty well, as it offers the same number of cores and threads as the current i7's, even if it can't clock as high. It is around half the cost of an 8700K though, and that money might be better put toward graphics in a build limited by budget.
As for the 2600's stock cooler, it will likely allow for some overclocking, but it's not as capable as the one that comes with the 2600X, so I would look for an AM4-compatible tower cooler for overclocking it.
And if you're running stock settings, an 8086K will be even more pointless, since it only boosts higher on a single core. For multi-threaded workloads, it boosts to the same clocks as an 8700K. And for overclocking, it only manages around 0.1 GHz higher clocks than an 8700K on average, which works out to about a 2% difference. And that's on average, as clock rates aren't guaranteed... some 8700Ks may overclock slightly better than some 8086Ks.