Either way, those playing on 4K are most likely to meet or exceed these hardware recommendations.
And more visible terrain means more bits independently animated (presumably) under CPU control, leading to increased CPU usage in typical 4K scenarios.
It's also possible that the "high", "medium", and "low" referenced in the article don't only refer to graphics, but also include important gameplay settings like map size and number of rival civilizations that can significantly affect average per-turn wall clock time required to process enemy AI on a given CPU, which IME is a considerably more important metric than framerate when it comes to the playability of any Civ game.
Also, I don't think gaming-optimized CPUs are that important. As far as I know, it's a concept AMD introduced in 2022. Until then, gamers usually just bought high-end consumer CPUs, and Intel users still do. And those use core counts to differentiate the top models from lower tiers.