This documentary is largely making a policy claim, that same-sex couples should have the right to be with their loved ones in the hospital and to make decisions regarding their health. This claim broadens into a larger policy claim that same-sex couples should have the same rights as heterosexual couples; the prior claim is merely a stepping stone to this.
The film makes a strong use of ethos, pathos, and logos. Charlene's story in general has a deep emotional appeal (pathos), and the use of music and images, especially from the funeral, also adds emotional pull to the argument. Using logos, the film compares homo- and heterosexual, showing similarities between the two; it also compares the same-sex rights movement to the civil rights movement, showing the similarities between those two. The ethos of the argument comes from who is telling the story and arguing for same-sex rights. Charlene, as a gay woman, knows her stuff; we hear her story and believe her to be credible, mostly because in sharing such an emotional story, the audience trusts her on a more personal level. The use of doctors and politicians opinions also adds to the credibility of the argument, because if these highly educated, highly trusted individuals believe in same-sex rights, we should, too.
I think the film had a very effective argument because of the strong use ethos, pathos, and logos. The repetition of Charlene's story also helps with effectiveness because now I will never forget her struggles.