The Mexican left has very little, until now, to do with the left in developed countries, which more than anything have decided to play by the rules of the democratic system, something that is still hard to accept for the constellation of parties and politicians that in Mexico align themselves on that side of the spectrum. And the reason for this is simple: the Mexican left is the daughter of the Mexican Revolution, which may have had many virtues, but for which the construction of a democratic society wasn't a priority. That is clear when you analyze the discourse of Plutarco Elías Calles, the founder of the PRI. Calles simply denied the possibility of the existence of a party opposed to the uber-party. The reason was very simple: the PNR and its descendants represented a revolution in which the people had expressed their will. Therefore, those who were opposed to the party were party of the non-people, the rich, the reaction, the "right", which by definition had no right to exist. This exclusive logic, which is shared by the great majority of revolutions, cancels from the outset any possibility of a democratic game. In fact, in the callista conception of politics, all ideological differences should be processed inside of the party. Therefore, if anyone differed from some policy in particular they had to express it inside of the party.
I'm presently reading a book called La Fractura Mexicana that aims to explain, among other phenomena, the same thing Chabat is talking about. I'm not quite far enough in to determine how closely author Roger Bartra's explanation resembles Chabat's, but so far it has a fair amount in common.