un vin - wine (n sg indef)

vinul - the wine (n sg def)

vinuri - wines (n pl indef)

vinurile - the wines (n pl def)

un pahar de vin roșu - a glass of red wine

It is neuter (masculine in singular, feminine in plural).

Actually 'a GLASS OF wine, two GLASSES of WINE" is quite specific and would translate to "un PAHAR de vin, două PAHARE de vin." To me this would be more like "a type of wine, two types of wine" in general or "a bottle of wine, two bottles of wine" if you wanted to be more specific and avoid ambiguity.

The countable issue has come up in comments before and it seems that "wines" and "fruits" are acceptable when one talks about several different types of wine or fruit.

I have said this before, that since this is a Romanian language course for English speakers, perhaps Duolingo should have come up with a standardized English language tree that could have then been translated to Romanian and other languages, and that perhaps would have eliminated some of these issues that come up with the more literal translations. That is, have an English-first approach to teaching a foreign language. That's what you would get if you purchased one of those travel dictionaries.

Anyway, wine does have a plural form as in:

"I love Australian wines, especially the white wines." https://dictionary.cambridge.org/dictionary/english/wine