No more relevant than eye color, since that particular doesn't control the right, which believe it or not extends to octogenarians with no possibility of procreation, sterile couples, etc. The equity of the law is found in it's treatment of each citizen, in the equality of right if you will.:thumb: Now make a case that a homosexual couple and a heterosexual couple are equivalent in the sense being discussed (procreation).
And, of course, the larger answer is that a homosexual couple may, in fact, procreate, if non traditionally. Or, they might adopt any number of children who are without parents. The latest studies I'm aware of appear to demonstrate they do a rather good job of it.
To the legitimacy of marriage? It's inarguably superfluous from a contractual perspective or as a founding necessity else.I fully admit that if you view procreation as superfluous (and an argument could be made) then the youtube video wouldn't be convincing.