Alright here is my quick thoughts on this and I may be off base but here it is.
Running logically makes sense for boxing it strengthens your legs and in boxing you are always on your feet so between running and your boxing drills you have a good base of cardio that is sport specific.
Now when you add MMA to the element I think that it is a different story in a MMA fight when you are defending the takedown, or looking for a sweep on the ground, or breaking your opponent down, or try to stand up after being taken down, or clinch work, I think those are more along the lines of your anearobic system so I think that burpees and Ross's style of conditioning has a good carryover.
That's just my opinion and I am open to it being shredded apart but to me it makes sense :icon_chee