Hello! That's is indeed extrange, the FFBot is extremely light on resources, it shouldn't really have a noticeable effect on other games, I sadly can't do much about it if it's a bottleneck on your CPU/GPU.
For future versions I guess I can put a performance option, but Im not sure if it's gonna do a whole lot, it hardly uses 100mb of memory, when I run a performance monitor, even when the numbers and damage gets on the billions for testing, My CPU usage doesn't go above 3%.
My guess is that the game you are playing is likely using almost 100% of your resources, and streaming + FFbot is putting it to the limit. When your game is the focus window, your PC allocates all the power on the game, leaving OBS lagging behind.