astringent:
1. Sour or bitter in taste.
2. Tending to draw together or constrict soft organic tissue; "astringent cosmetic lotions"

Still thinking about the "why" of "dry" for non sweet wine. it might be this: (but may be no news to anyone)

Dry: used as in absence of...

From Merriam Webster:
l4 obsolete : involving no bloodshed or drowning <I would fain die a dry death -- Shakespeare>
5 a : marked by the absence of alcoholic beverages <a dry party> b : prohibiting the manufacture or distribution of alcoholic beverages <a dry county>
6 : served or eaten without butter or margarine <dry toast>
7 a : lacking sweetness : SEC <dry champagne> b : having all or most sugar fermented to alcohol <a dry wine> <dry beer>