I think most games have orthogonal twitch and strategy components. All games of course have some strategy -- even decided games like Checkers have the optimal strategy, along side unoptimal ones.
There are "action" games (high twitch) that have very high strategic content. The kicker is that sometimes twitch can serve as a ceiling for strategy. That is, below a certain twitch level, some strategies are not viable or available. Games with very low twitch minimize this, like turn-based RPGs and strategy games. But even StarCraft requires high twitch (aka unit micro) to execute some strategies!
Even ostensibly twitch based games have a lot of strategy. 2D fighters have tons of strategy, so do games like * Souls. Stealth games also require good strategy and spacial reasoning coupled with strong execution.
There are "action" games (high twitch) that have very high strategic content. The kicker is that sometimes twitch can serve as a ceiling for strategy. That is, below a certain twitch level, some strategies are not viable or available. Games with very low twitch minimize this, like turn-based RPGs and strategy games. But even StarCraft requires high twitch (aka unit micro) to execute some strategies!