The 7700K, especially overclocked to 4700 MHz or above, is as of yet no slouch at anything, unless craving perhaps 144 Hz minimums in some of the latest games, where the CPUs with more threads often have an advantage in both minimum and average FPS...
If craving live streaming in addition to gaming, the 7700K's 4c/8t design is not enough, go for the 3700X!