As addressed in other comments in this thread and past threads on this sort (when the paper came out), it is not bubble sort. Bubble sort only compares adjacent items and swaps them if they are in the wrong order. This has the effect of "bubbling" the largest value to the top (the way it's often written, could also reverse it to push the smallest down first).
This sort is like a worse performance version of insertion sort. But insertion sort creates a partition (and in doing this performs a sort) of the first i+1 items, with i increasing until the entire sequence is sorted. This one will scan the entire sequence every time on the inner loop instead of just a subset of it and usually perform more swaps.
This sort is like a worse performance version of insertion sort. But insertion sort creates a partition (and in doing this performs a sort) of the first i+1 items, with i increasing until the entire sequence is sorted. This one will scan the entire sequence every time on the inner loop instead of just a subset of it and usually perform more swaps.