I don't know that this qualifies as unbelievable. This is just good marketing and spin. The image in that link is exploiting the fact that modern codecs specify upsampling filters, so the HEVC half looks smoothly varying while JPEG can, per spec, only look pixelated when blown up like that.
There's absolutely no reason that thing couldn't have shown you a jpeg image rendered with bilinear filtering, which of course is what you'll see if you put that JPEG on a texture and scale it up using the GPU.
But it didn't, because it wanted to convince you how much "unbelievably" better HEVC is. Meh.
I mean, to be clear: HEVC is absolutely better, to the tune of almost a factor of two in byte size for the same subjective quality. Just not like this. If you've got a site where still images are a significant fraction of your bandwidth budget (and your bandwidth budget is a significant fraction of your budget budget) then this could help you. In practice... static content bandwidth is mostly a solved problem and no one cares, which is why we aren't using BPG.