The best action games like Shadow of the Colossus are Ico, The Last Guardian and Praey for the Gods. Below are 8, each with the reason it is here — and, at the end, what filtering to action costs you.
Filtering to action means you want the fighting to carry the game rather than the story or the map. It is the right filter when what you actually miss is how something felt in your hands.
What you get: Combat you get better at. Action games put their design budget into the moment-to-moment, so the thing you are doing in minute two is the thing you are still doing in hour twenty, only better.
What made Shadow of the Colossus worth playing in the first place is covered on the full list. This page is the action part of that answer, and only the action part.
Same director and the same restraint — an empty castle, one companion, almost no dialogue.
Team Ico's third game: the colossus is on your side this time, and it does not always listen.
An unashamed homage — climbing huge bosses in a frozen open world, plus survival mechanics.
Boss rush distilled: one arrow, one hit, sixteen puzzle-bosses in a quiet overworld.
The long empty traversal between objectives is the game, not the filler between it.
The closest big-budget game to that feeling of riding into somewhere nobody has been.
For the boss-as-landscape scale, if you want the combat to be genuinely hard.
Traversal as the entire pleasure, punctuated by five enormous hunts.
Pacing and world. Action games rarely have the quiet stretches or the writing that the adventure and RPG picks bring, and a few of them are shorter than they look.
Specifically, these are strong answers for Shadow of the Colossus that are not action games, so they are not on this page:
The full list is on games like Shadow of the Colossus — 11 picks, no genre filter.
Ico. Same director and the same restraint — an empty castle, one companion, almost no dialogue.
No. Shadow of the Colossus released on the PlayStation 2, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
A small set of verbs and a game that keeps finding new questions to ask of them. The weak ones add buttons instead; the strong ones make you better at the ones you already have.
No, and difficulty is a poor proxy for depth. Some of the hardest action games have very few decisions in them, and some of the deepest have a difficulty setting that lets you meet them halfway.
By hand. Each pick was written for the full Shadow of the Colossus list first, on what the game actually does, and this page is the part of that list that is action — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the action guide for where to start in the genre generally.