I think the major difference is this notation has the count of loose wires corresponding to dimension, and Penrose notation has the count of loose wires corresponding to tensor valence.

Here, a diagram with 1L and 2R wires corresponds to a 2d-vector, in Penrose's notation it would correspond to a (1,2) tensor that takes kd-vectors to kXk matrices.

But... they certainly have a similar feel. I wonder if you could build up the Penrose notation out of this.