I have only the roughest knowledge of Japanese, but it's to my knowledge that while "musume" does mean "daughter," it's also used to mean "girl," though if it's intended to be a more casual usage or to try and differentiate it from a word like "shoujo" is beyond me.
With all that being said, with this game being Western-made, I find there to be zero reason for them to say musume instead of just girl. Maybe they want their game to stand out amongst other games that are titled Monster Girl [third word], but it's a rather lazy approach to it.
I'd blame the developers for trying to go the extra weeb-y mile with the usage of "musume." "Monster musume," as far as I know, is the easiest way to say "monster girl" in Japanese. It also doesn't help that the series "Monster Musume" is just shorthand for the full name "Monster Musume no iru Nichijou" (Everyday Life With Monster Girls), which is pretty damn lengthy, thus the reason for the shortening. Another example of the term's usage is how to an English-speaking audience, we call the ever-(in)famous game "Monster Girl Quest," but in Japanese the title is "MonMusu Quest," with MonMusu just being a cutesy shorthand for "monster musume" (and thus just going back to meaning monster girl). So the manga series and its anime adaptation didn't invent the term, just popularized it.
(Heavy apologies for my abuse of parentheses and quotation marks here, lmao.)