For instance, instead of a3 at the end of that, White can go Rg7, and taking the rook spells disaster because after Black gives up the bishop with Bxg7 fxg7 Rg8, White can sac a knight or bishop on b5 and then crash through on d6. But even if Black doesn't take the rook and just tries to push b4, then Nd5 is very strong. So a3 turns out not to be necessary.
I can't remember as much as I'd like about the 13 ... Nc5 line. But the brief answer is that, partly because lines like the one you gave, the whole 13 ... Nc5 line has been out of fashion for a decade or so, largely in favor of the unintuitive 13 ... 0-0, an idea of Ju Wenjun's, which she and others have shown to be surprisingly not suicidal.