Happy Birthgay is an expression which commemorates someone's anniversary. It can be used as follows:
a) a modified version for wishing happy birthday to an openly gay friend;
b) in order to tease someone you assume is gay but has not come out yet; the objective here being simply to check the person's reaction. Should he/she feel attacked, one can always claim it was a typo;
c) in order to actually celebrate the annual coming out of a gay person.
Fred: Man, yesterday's party at Alex was wild, and I mean W-I-L-D! I just can say: "Happy Birthgay, Alex"!
Marc: Yeah man, I feel you, birthgays are always like that! Often it takes'em a while, but once they come out: watch out!