I don't think you should be looking at the tenses if you want to know the differences between these sentences. The first option is wrong.
*They might have died. (If you wanted to use "have been" => They might have been dead.)
Look at "might." In this situation, "might" is equal to "maybe." It's uncertain. We do not know if they are dead, but there is a possibility that they are.
They must have died.
"Must" indicates something that is logically likely, something that's very nearly certain. They have to be dead; that's what makes more sense.