No one is claiming that this sort algorithm (or any other) is asymptotically faster than O(n log(n)). It can be mathematically proved that no sort algorithm can improve on this. The object with sort algorithms is to find one with good constant-factor performance on typical inputs.

Frankly, I am more persuaded by the arguments in favor of an algorithm like "Tim-sort", which doesn't claim to micro-optimize hardware more efficiently (that's basically what "better swapping" is claiming), but instead claims that the algorithm is particularly efficient on some commonly-seen patterns (like "partially-sorted", or "pieces of the list are reverse-sorted"). Of course, any kind of argument about why one sort is better than another are inferior to actual benchmarks.