What would a game be that didn't have client side controls?

I left some implicit context out:

Games that are highly competitive and rely on client-side controls (like aimbots)

Games that are highly competetive in how they react to precision and immediacy of client input, and thus are sensitive to tools like aimbots, ...

In Chess or Poker, it doesn't matter how fast/slow/precisely you click the game window. In Mech Warrior Online, it's less important than in Unreal Tournament. MWO can still suffer a bit from aimbots ("cored every time") but not as much as UT.

Okay, that makes more sense, to rephrase: basically design around it such that wins aren't solely determined by the swiftness/accuracy of the input of the players controller.

(And League of Legends could suffer from this, skillshots in particular could theoretically be hacked to always hit when invoked, or auto-flash to avoid incoming projectiles. Granted the sheer amount of different abilities and effects would make it difficult to make useful)