Of course she saved Regina's happiness, because she saved Regina's life. That's also another thing that doesn't have to be an either/or. Regina can't have a happy ending if she's had all the light snuffed out of her by the darkness or if she's dead before she's fully attained whatever her happy ending is.
Emma also saved everyone else's happiness because she saved everyone else's lives. Right now, the people who love Emma are miserable, but is there any doubt that they're going to save her? So their happy endings, along with Emma's, are still attainable, too. If the darkness consumed everyone and everything, no one would have a happily ever after. If this was the series finale, I would be a lot more angry about this whole thing, but it's not. It's a season finale, so this isn't the end of the story.
The writers may have a Regina bias but I don't think it's as all-encompassing as it's frequently made out to be. Just like there are shipper goggles, I do think there are anti-shipper or anti-character goggles and sometimes what we see and hear gets filtered through those goggles, too. The fact of the matter is they wrote this big massive heroic moment for the savior, and we're sitting here debating whether or not it was all because of one person. I personally don't believe it was. The actress who plays the character has gone on record multiple times to say she doesn't believe it was, that her headspace when playing the scene was that Emma was saving everyone. One of those times was during a panel where the writers heard her and didn't jump in to correct her or clarify. Regardless of what Eddy said in one interview, the story as played out onscreen did not indicate that it was.
Basically, I think we're all making a mountain out of a molehill, here, on all sides. Emma's sacrifice wasn't just for Regina, but the fact that Regina was included or even highlighted isn't a huge deal to me, either.