The big CPU-bottlenecked esports game is CS:GO, or any other Valve / Source game. Even on an older CPU with mediocre single-threaded perf (i7-5820K), I can run the game fine on high settings, 1080p (100-250fps), but it occasionally dips down below my 144hz refresh rate, which can be annoying.

And yeah, the GPU is never begged while playing, but multiple CPU cores definitely are.

Also, emulation is another big place where CPU bottlenecking is a thing. Look at Dolphin (Gamecube/Wii), Citra (Wii U), and yuzu (Switch), they're all CPU bound. Folks in the various subreddits will ask why their new GPU isn't netting them a higher framerate, and it's because the GPU is almost not even used (though in some cases with better graphical effects, shaders, etc. they can be beneficial)