The word ‘gamey’ has a meaning in regard to food. But what about table top roleplaying?
I’d suggest the idea that some mechanics is ‘gamey’ is much the same as the concern some folk express in regards to snakes being classed as prone in a game system.
Ie, they don’t imagine snakes can be prone – therefore it’s ‘wrong’ for that to be the case. Further it’s about fiction (their idea of fiction) coming ahead of rules. Rather than rules coming first and fiction should shape itself to conform to the rules. Anything that tries to have rules that the folks fiction will have to conform to…it’s ‘gamey’. The idea of the game mechanics having a strong control over what happens in play…it’s anathema.