A modified version of the algorithm is used in the US for matching graduating medical students with hospital positions. It's interesting topic ( https://en.m.wikipedia.org/wiki/Match_Day_(medicine) )

Almost, but not quite.

For one, the male class is not given any opportunity to rank females, as it is presumed that most males would attempt to game their own preference rankings to maximize their chances at getting a match. Secondly, the classes are not closed, and additional members may be added or removed at any time, when some matches may already be dating.

To be sure, whomever it is that figures out the fair dating algorithm would have to cite Gale-Shapley as a starting point.