It is incomplete. It does not explain why f(g1) = f(g2) implies [g1] = [g2] for any g1, g2 in G, which would require showing that Ker f is always a subgroup of G. It also does not expand the normality / conjugation argument that makes multiplications inside G/Ker f well-defined. Since that would also require discussing inverses, it would be too much text for a simple visual aid.
I think it turned out cute tho