The linked talk explains that death isn't necessarily related to adaptation. There are many advanced organisms that just keep splitting and don't die, unless eaten or something. Moreover, the part of ourselves that accumulates adaptations (the line of germ cells passed from parents to children) also keeps splitting and doesn't die.

Rather, the point is that at some point the immortal germ line found a weird trick: "let's make in each generation a bunch of cells that will help the germ line reproduce, but that won't themselves reproduce". Like sterile worker bees. And our body, including the brain, is a pile of just such disposable cells.