The best adventure games like Dragon Warrior Monsters are Dragon Quest Monsters: The Dark Prince, Pokemon Emerald and Cassette Beasts. Below are 6, each with the reason it is here — and, at the end, what filtering to adventure costs you.
Filtering to adventure means the place and the story are what you want back, not the challenge. It is the right filter when the thing you remember is where you were rather than what you did.
What you get: A world with a reason to wander it, and writing that survives being read rather than skipped.
What made Dragon Warrior Monsters worth playing in the first place is covered on the full list. This page is the adventure part of that answer, and only the adventure part.
The modern entry, and the breeding system is intact.
The generation with the Battle Frontier, if you want the other approach.
The best non-Pokemon monster collector, with a clever type system.
Straightforward, funny, and full of creatures to catch.
Creature collecting with real depth in the battles.
A faithful classic-style monster RPG with modern quality of life.
Mechanical depth. Several of the best adventure games have combat that is deliberately unsatisfying, because they want your attention somewhere else.
Specifically, these are strong answers for Dragon Warrior Monsters that are not adventure games, so they are not on this page:
The full list is on games like Dragon Warrior Monsters — 9 picks, no genre filter.
Dragon Quest Monsters: The Dark Prince. The modern entry, and the breeding system is intact.
No. Dragon Warrior Monsters released on the Nintendo Game Boy, 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.
Anywhere the story and the place matter more than the skill ceiling — point-and-click, walking sims, narrative thrillers and most open worlds. The label alone tells you very little, which is why each pick here says what it actually is.
They split hard. Open-world adventures run to a hundred hours; the narrative ones are often finishable in an evening, and the short ones are usually the better written.
By hand. Each pick was written for the full Dragon Warrior Monsters list first, on what the game actually does, and this page is the part of that list that is adventure — 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 adventure guide for where to start in the genre generally.