From my understanding of Sociology class or maybe it was in Psychology , all living beings with a brain have REM sleep.
Its funny, one of my dogs used to sleep laying on its side. And in the middle of the night would start growling. I would go over to him and he would be growling and his legs would be moving like he was running haha. I could only imagine he was chasing a mailman in his dream hah.
ROFLMAO!!! One of my mastiffs has battles in her sleep too! She barks, growls, runs, jumps... It's a trip! If dogs can do it, I'm sure beardies can too.