Meowth's association with coins and wealth comes from many ancient societies where their annually discarded forehead bones were used as a form of currency. In modern day, they have no real value but are occasionally kept as souvenirs by Meowth owners who wish to document their Pokémon's growth.
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Though given that all Pokemon hatch from eggs and none (except maybe Miltank) appear to produce milk for their young, I have to wonder if certain Pokemon can be truly classified as 'mammalian' - though I know your use of the word is more a description of Meowth's furry, presumably warm-blooded physiology. I have so many questions about how taxonomy works in the Pokemon world.
Long story short- you're right, Meowth is being described as mammalian due to its superficial resemblance to cats and not because its biology actually lines up with what we know "mammals" to be. There isn't really a better word for them, unless I want to invent a bunch of fictional biological classes. And I seriously don't have time for that (plus they'd all probably sound silly and made-up).
If you're curious about the basics of Pokémon biology, I do go into it in more detail in the full Pokémon anatomy textbook.
It's not currently available yet, but Patreon supporters get a 65 page excerpt that (among other things) describes Pokémon eggs in more detail
Wish I could, but I am unfortunately a broke grad student. Might start saving for when the book comes out though, 'cause it looks really cool! ^_^
More seriously, that does seem to be the extent of taxonomy in Pokémon, they don't really have species groups in a way we'd recognize. (Though they do have groups of Pokémon who can only reproduce with each other, a guy named Saphroneth figured out that aside from the asexuals any given Pokémon could potentially have any Pokémon in its ancestry.)
I suppose it might have something to do with Mew being the common ancestor of all other Pokemon and being able to use every move? I dunno. It is ultimately a game/show and I'm overthinking it, but it's fun to theorize.