I'm sure that if you ask most people on here if gay people deserve happiness they would all say the same thing. So let's instead look at the issue on the video, which basically comes down to gay people being unhappy lieing about their sexual orientation to friends and family because they are too scared of getting kicked out of their homes. This is a big problem in the US where teenagers have come out to their parents, who have then kicked them onto the streets.
My ex-partner is in a situation like that where he is gay but his parents are homophobic and he's scared of coming out to them for fear of them disowning him. And sinch he still relies on them both financially and emotionally, we can't afford to take that risk. When I met him he hadn't come out to anyone, and I was the first person he came out to when he said he loved me. That was one of the hardest things for him to do but once he did, he started coming out to some of his other close friends and you could see the change in him. He was a lot happier being able to be himself instead of living a lie.
I'm lucky that my parents are very accepting, and I live in an area with a very open Gay community, but I understand how hard it is for those who aren't as fortunate, and have to live a lie and therefore cannot be truly happy.