I don't particularly care to play a game about sexuality, which is the only real reason I can imagine having a specifically gay protagonist would be (ie. where their sexuality is an important element of the plot).
In Mass Effect 3, Jade Empire, DAII and perhaps a handful of others where a homosexual relationship is possible, I don't know if the OP's friend would consider these to be "sufficiently" gay protagonists, particularly as they are only what we allow them to be. In both cases, sexuality didn't define the protagonist (mostly because we did much of the defining ourselves) or play a role in the story.
If the sexuality is important, I personally wouldn't really want to play it, regardless of orientation. I'm not interested in a game about politics, gender issues/equality, sexuality, discrimination, race relations, etc. If it isn't important, then what difference does the protagonist's sexuality make?. That's not to say I wouldn't mind playing a game in which there are racists, homosexuals/homophobes, sexists or feminists, provided that it is background and flavour and not front-and-centre/driving the plot.
My question then is this. If a protagonist is established as gay at the very start of a game, but no mention or reference to such is made thereafter, nor is there anything about sexuality or even any relationships to pursue, what would the OP's friend say on that? And why would a protagonist need to be specifically gay and able to be decided by the player? It kinda makes it annoying for players who would prefer to play a straight protagonist.