Taking a quick look at the paper...

Their claim isn't that the brain uses gradient descent, but that the direction of updates has (on average) positive inner product with the gradient. I expect this would also be true for (say) simulated annealing, yet we don't say that simulated annealing is gradient descent.

There's also a discussion of loss functions and how they relate to the update missing - as far as I know, there's still no great notion of how the brain picks a global loss function, and no mechanism for backprop. In this paper, looking at a specific learning task you can define a loss function extrinsically allowing us to talk about the gradient, but how that relates to things happening in the brain is a big big mystery.