Metroid, Half-Life, and Demon's Souls I would take issue with, but I've always considered Zelda a puzzle game, and I never questioned it until now.
I suppose the new Breath of the Wild / Tears of the Kingdom titles are more action-oriented, but everything in the mold of Ocarina of Time is a puzzle game with some light combat sprinkled on top.
Dungeons contain mainly puzzles, but otherwise it's a lot of combat and story and side quests, similar to most RPGs.
I was being a bit silly but the Souls series do have a metroidvania angle to them. Also each enemy, especially the bosses, are small puzzles where you figure out how they work and then how to overcome them.