They do mention Penrose notation in the linked arxiv paper[1], as well as Cvitanović's Birdtracks[2] which let you do calculations on representations of groups.
They claim they're making it more accessible with pedagogical examples (and innovations in representing differential vector calculus).
I still prefer index notation. Their notation looks pretty intricate and I think it would be really hard to do long calculations in it. It's also not clear to me how you'd generalise it to non-commutative vector algebras like in quantum mechanics.