First, it's apples and oranges. Brenner is not offering an account of the capitalist system as such in its abstract form--Marxism. Brenner is giving a historical materialist account of the current "crisis" (or whatever you want to call it--Marx couldn't be, at least in any direct way. Yeah, yeah, Marx may have insight to offer into the current crisis. Brenner thinks so. But he can't talk about Bretton Woods, the Golden Age of postwar Capitalism, etc., because these things hadn't happened yet.
Second, Rakesh misses Brenner's real targets, which are clearly set up in the piece, notably the profit squeeze and underconcomputionist explanations of the "crisis," as well as the new long boom fans and those who seek noneconomic explanations of the end of the Golden Age. For these purposes it's not necessary to offer an explanation of fraticidal competition. He can take it for granted. One has to start from, some premises--as Marx did with certain postiltes about value.
Third, I am not sure why the fratricidal nature of competition needs a need explanation. Maybe I was bittem too early by game theory, but I would have thought that prisoner's dilemmas and collective action problems guarantee that competition is going to be fratricidal rather than friendly whenever it's serious. But pay no mind to me, I'm just a flatheaded Analytical Marxist.