have not dug into the paper, but basically if it can be shown that NP cannot be computed with Poly-size circuits, then P!=NP, ie a weaker consequence of the stronger NP!=P/Poly. that is one of the basic conjectures of circuit theory, a stronger statement than P!=NP. the author may be talking about P-size circuits without mentioning the P/Poly class by name-- that would show some unfamiliarity with standard complexity theory, but is not a huge crime, and it is conceivably not necessary to actually refer to P/Poly in circuit proof referring to that class, although of course it would be better... P/Poly was originally defined w.r.t an Oracle, and arguably the equivalent characterization of that same class as "P-size nonuniform circuits" is actually much simpler & intuitive & natural....