I don’t think there’s a hard requirement of having a running mate. In fact, it would probably be much more appropriate. In totalitarian environments, as soon as you cut the head off the snake, and the power vacuum is created, it won’t really matter who the VP is as it will be an internal war anyway.
I mean, to be fair, the Nazis killed a lot of Nazis. They really just like killing people. Kind of what they were known for, and probably what they will keep doing.
It’s a rather unhealthy mindset these creatures have.