1) Except for OSU that I don't know all the other games are single threaded and will run worse if not very badly on the 2600x
2) If you have decent upload speeds you can stream by using the iGPU or your discrete GPU which won't slow down your CPU at all.
3) Even if you want to use your CPU, 720/60FPS and 1080/30FPS don't need as much CPU power as people seam to believe,and those games using only one thread would leave plenty of cores for the streaming even for 1080/60FPS.
i5-8400 would be the better choice of the two,but for starcraft/total war even a higher clocked intel would be better.