Vintage means primarily “the yield of wine from one particular year”, but as an adjective, it started to be used for anything that is “like something old and high quality”, e.g. “vintage guitars”.
Although it looks slightly like “vine age”, there is no etymological connection between “vintage” and the word “age”, and there is also none in the pronunciation, because “vintage” is pronounced /ˈvɪntɪdʒ/ (vin-tidzh)
However, etymology is probably hardly an argument here, because “vin” in “vintage” is in fact related to “vine”, even though it is pronounced differently.