You're correct that it has a significantly bigger impact in reaction-dependant games. [1] Civilization 6 was just a good example of a CPU-heavy game, regardless of whether those frames are that useful. However there's also the case of normalization. After using a high refresh rate monitor, even something as simple as moving the cursor in Windows feels laggy with lower refresh rate monitors.

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[1] This being all reaction-dependant games, doesn't have to be FPS. Even fast paced pong qualifies.