I'm with Ventifact on this. Would you call bungalow a Hindi word? It is a loan word from Hindi. What about disco? It is borrowed from French, but shortened from its original form discotheque. Actually what is an English word, as many or most common words are derived from Latin or Norman French, and some from the Celtic languages? Kindergarten, schadenfreude, sauerkraut and angst are English words with German roots.
(Five years and he doesn't learn to not leave the soda in the fridge?)
I would've drank the free soda instead of bringing my own. Once, I got two from a vending machine when I only paid enough for one. Mystery as to how that happened, though.
How it became an English word is different than if it is an English word. Note also the context of whether this word was an English one: you said you knew it because you knew German, I pointed out knowing German was not necessary. In fact I learned the word a few years ago from a friend who speaks no German. And also I don't have any reason to expect people speaking German refer to schadenfreude more often than do speakers of other languages, by whatever term each language offers. So many English words are loan words that it is nearly trivial to point it out. Yes it is an English word. Yes it is an English loanword. Yes it is a German word (capitalized of course), and was a German word before its English adoption. Yes: it is an English word.