I'm thinking of super fast-paced games like Robotron 2084 or Bouncing Babies. Normally I thought of them as twitch games, but with Nintendo Twitch and twitch.tv, that word just don't work anymore. But what should I call them instead?

Maybe "Reflex Games" or "Dexterity Games" could work?

It's the Nintendo Switch, not Twitch.

But yeah, nowadays if something was referred to as a 'Twitch game', I'd assume it was a parade of jumpscares for people to unconvincingly overreact to rather than something that requires reflexes.

So reflex game would probably be a good replacement.