Good question, and one I don't quite know the answer to. But here is my reasoning, such as it is...
First, on a personal level...
a) I'm not gay, and yet it spoke to me about love, and I certainly identified with the characters and with the love, denial of love, fear, loss, etc., so perhaps that means it was universal. Except...
b) I have a history of liking gay love stories better than straight love stories, and responding to them more strongly and getting more obsessed and finding the whole thing somehow more beautiful than if it was about a man and a woman. So perhaps that means it was a gay love story. Except...
On a more intellectual (trying to be) level...
I think, like many gay love stories, it is really about forbidden love. And that, in turn, can be and IS universal. Someone very clever explained it to me one time. Some love stories reinforce the societal standards... like Shakesperean comedies where everyone gets married in the end, or chick flicks... and some love stories, the really BIG and more powerful ones, go against the societal standards and transcend them and eventually (but usually not till after a tragedy) change them. And that's what I really think BBM is.
Short answer:
Universal.