The title pretty much says it all: Does Charm Monster work on Humanoids?

My player tried Charm Monster on an elf, the spell says it works on any "creature", which I interpreted to mean any living thing so I let them do it. Am I understanding it correctly?

Yes.

The spell says: "You attempt to charm a creature you can see within range."

Any creature, no restrictions, even constructs, undead, fiends, elementals, etc.

Yes it works on any creature 

Edit: I believe “creature” is a generic term for pretty much everything so it should work on constructs and undead as well

Charm person = only works on humanoids. Charm monster = works on any creature, including humanoids.

Humanoid is a subset of Creature, so yes.

Charm Monster works on anything you find here: https://www.dndbeyond.com/monsters

Charm Person only works on https://www.dndbeyond.com/monsters?filter-type=11

Quote from ThriKreenWarrior >>

Yes it works on any creature 

Edit: I believe “creature” is a generic term for pretty much everything so it should work on constructs and undead as well

 This is correct, Creature is a general term and encompasses anything that is not an Object. Note that a spell like Command can target any creature and then has specific language that it cannot affect Undead. Another example is Animate Objects, it targets Objects and turns them into Creatures of the Construct type and describes their Ability Scores and other statistics.

Quote from Fangeye >>

Creature is a general term and encompasses anything that is not an Object. 

 But the sky isn't an object or a creature.  ;-)

Quote from Farling >>

Quote from Fangeye >>

Creature is a general term and encompasses anything that is not an Object. 

 But the sky isn't an object or a creature.

 So it’s a point in space, for those spells that target such. So I guess creature is everything not an object or a point?