Sesame Street, Sparse
Did you notice the sort of sunny, PBS kiddie show-style banter between the characters? Because that thought came to us when we heard Vladimir ask:
VLADIMIR
Do you want a carrot?
ESTRAGON
Is that all there is?
VLADIMIR
I might have some turnips.
ESTRAGON
Give me a carrot. (Vladimir rummages in his pockets, takes out a turnip and gives it to Estragon who takes a bite out of it. Angrily.) It's a turnip!
VLADIMIR
Oh pardon! I could have sworn it was a carrot. (1.253-7)
It sounds just like a warped Big Bird. Today's Beckett play was brought to you by the letter "C," for carrot! And the number "2," for duality!
But if you need to put some academic jargon-esque labels on the style, we would probably go with "sparse," "minimalistic," or, if you were feeling ready dangerous, "barren."