I've seen him do it both ways, complete stand up and just going from deck squat to plyo push up.
I like to stand all the way up, and I do a back fall, into a deck squat, for Jujutsu purposes.
Now that's an interesting variation. I'm generally working on my concrete garage floor, but might have to bring out the mat and try those sometime.
I'll try 'em both ways; I already do burpees, so I may prefer not to stand for these. We'll see.