Yeah. I consider high level RTS and fighter competitive play to oftentimes have puzzle-elements sprinkled into what seems like a fully chaotic, pure-game environment.
e.g., “Ah yes, he is choosing a 14-hatch, speedling expand with eyes on the gold and gas for roaches on Metropolis. The proper counterplay here based on my current position [no expand, no gas, reactor already building on my barracks, 3 away from supply cap, 47 energy built up on my Command Center] is obviously 7-rax Reapers until the game ends, one way or the other.”
But then you mix in the dexterity elements (extremely perfect control can win out situations of immense strategic disadvantage. For instance, sufficient quantities of splash-damaging Siege Tanks were often seen as a hard counter to masses of one-shot, one-kill Zerglings in TvZ. However, you had interesting things like AI controlled play revealing that zerglings could be split so perfectly as to trigger the targeting AI of the siege tanks to make their shots do very sub optimal spreads of splash damage, allowing far more Zerglings to survive than previously thought feasible. And indeed, slowly over time, humans began to master those talents themselves. This is oversimplifying the evolution of strategies a lot and contains some inaccuracies, so sorry to my fellow competitive SC2 nerds).
And of course there’s also the competitive element: as people would master strategies and counter-strategies in the old Brood War days, sometimes the counter-strategies would become so fixated and focused that players would uncover novel, oftentimes otherwise considered sub-optimal responses that would turn the matches on their head, introducing a whole new “optimal” meta-game, and so on and so forth, such that a game that received no balances patches after a certain point was still seeing wild shifts in optimal strategy a decade after release.
But after beating up my own argument so badly, on some level, extreme top-tier high level competitive play in some genres–where “sufficient dexterity” can be assumed and the meta-game is not relevant to an individual match–the multiplayer matchup takes on a strong appearance of being a puzzle-game, to the point where commentators can often “call” a match minutes before its conclusion, based purely on the build orders or scouting patterns used.
More or less ditto for some matchups in fighting games. “Assuming perfect, Armada-level control of that Fox, the only way for my Jigglypuff to succeed is to initiate Strategy such-and-such with equally perfect control until I chip him down from an effectively perfectly defended position, since I can assume he will not try deemed-suboptimal approaches/offensive strategies that have long been discarded by the competitive community, instead relying on optimal strategies that my counter-strategy effectively neuters.”