In a cursory reading, I think I can address these criticisms. Although one would have liked the author to call out each in his introduction.

Naturalization: This proof is not combinatorial, it is based on a model of formal logic. This is addressed by the author directly.

Relativization: This is proof by contradiction and relies on understanding the solution space of k-SAT instances, not on diagonalization.

Algebrization: This proof looks beyond the size of small circuit into how the circuit inputs interact and how this interaction spreads throughout the circuit.