Oof, there is a lot to unpack here, primarily because I fear this question comes via the belief that there is a correct, and an incorrect, way to drink wine, to which I call absolute BS. If that bottle of wine you are drinking is your bottle, and you paid for it, you get to decide the glassware you use to serve it in — and the way you treat said glassware.
That said, it is correct that you don’t need a coaster for your glass of wine, as long as that glass is stemware, which wine snobs will tell you it should always be, but which I will tell you can be a pint glass if that’s your damn preference!
But, if it’s a stemmed wine glass, the stem prevents condensation from forming at the base of the glass, so you don’t need a coaster the way you would for a highball glass or a pint of beer. Then again, not everyone is the most refined sipper, and it’s possible some wine could run down the side of the glass, along the stem, and to the base, leaving a nice red ring on your coffee table. So if you want to protect that table with a coaster, go right ahead.
