Well I do think the 2 universes have to sort of match.
Of course when I first saw it without reading the extras I just thought it was sent back in time in the same universe and that he had to sacrifice himself to keep everyone else alive.
Yes, it appears that if he was killed that someone else would have been the chosen one. However Frank is not who did the choosing. Frank is killed in the alternate universe and becomes the Manipulated Dead as does the girlfriend. These people can time travel and their only goal is to get the chosen one to guide the artifact back.
So had Donnie been killed then it probably also would have meant that Frank would not have been killed. Some other person(s) might have become Manipulated Dead and sought to force the other chosen one to guide the artifact back.
What allows the movie to escape some problems is by leaving that "Why?" as unknown with regards to why this happens and why a certain person is made the chosen one. The story leaves those aspects as unresolvable.
Doesn't bother me anymore than not having a solid explanation as to why a super spiderbite would allow humans to stick to walls.

Most fantasy/SF films require at least one unresolved alteration to set everything else in motion. To me the point is more to watch the dominoes fall than it is to understand why they were setup in the first place, if that makes some sense.
Studying the human condition is a lot about watching human reactions (or imagining them) in a variety of situations. Sometimes we get funny results when the situations are fake but mostly the artist will still be pointing out some real piece of humanity by how they have the characters react.