If you bring activation sparsity into the mix, the advantage of SNN processors over GPUs/TPUs becomes more clear. Loss-gradient-based optimisation approaches are great because they give you a tool to include e.g. sparsity regularisation into the loss. Encouraging sparse activity makes simple linear algebra a poor fit for network activation, and SNN processors a much better fit.

I agree with these points, however the main advantage of the method presented in the paper is precisely that both the forward propagation and backward propagation can be seen as being performed by a network operating on temporally sparse events. We absolutely had event-based sensors and control as a motivation in mind. The fact that you can write down the connectivity of the neurons in terms of a weight matrix, does not mean that it can't be sparse. Since you are actually processing one spike at a time (potentially asynchronously), you don't need to implement any matrix multiplication. Current neuromorphic hardware achieves at least some degree of sparsity in their synaptic crossbars (BrainScales2, Spinnaker) or largely eliminates them like Loihi.