The page mostly talks about image resampling where the goal is more or less preserving all frequencies, but it's also extremely effective at implementing Gaussian blur. Basically, you do n iterations of sampling by 1/2 using this kernel, followed by a very small FIR filter, then n iterations of upsampling 2x using the same kernel. Here, n is essentially log2 of the blur radius, and the total amount of computation is essentially invariant to that radius. All these computations are efficient on GPU - in particular, the upsampling can be done using vanilla bilinear texture sampling (which is very cheap), just being slightly clever about the fractional coordinates.

It works well because, as stated, the kernel does a good job rejecting frequencies prone to aliasing. So, in particular, you don't get any real quality loss from doing 2x scale changes as opposed to bigger steps (and thus considerably larger FIR support).

I have some Python notebooks with some of these results, haven't gotten around to publishing them yet.