dameeji is a loanword, no? I have no ability in japanese but from a quick search 損傷 Sonshō (injury), which includes 傷 Kizu (scratch, wound, scar, weak point, hurt) seems like the words for "Damage" in a transliteration sense.

I'm just surprised there is no native (non-loanword) word for "damage" in japanese

There are a ton of words where the loan-word is commonly used even when there's a native word.

For example, there's both "desuku" for desk, and also "tsukue" (the original japanese word). They're both in very common use. The loan-word has an ever-so-slight vibe of a western-style desk, while tsukue has an ever-so-slight vibe of a schoolroom desk.

Languages change over time, and english has had a large influence on Japanese.

Of course there's a word for damage in japanese ("higai" is probably the best fit for Magic), but there's also "dameeji" now, and it feels mildly more western-fantasy like to use it.

There isn't always a logical or obvious reason why a loan-word is used over a native word, as is true for a lot of linguistic changes (like in english, why does someone say "soda" vs "pop", why do some people call it a "pillbug" and some a "rolly-polly"?). Just accept that loan-words are used in some cases, and there's not always a reason other than "people just say it that way".

I'm happy to accept it, I just didn't expect it. Like I say, I don't know foreign languages enough to speak them or know their culture, I find them interesting from a linguistic point of view. (also its a "soft drink" and a "woodlouse" :P )