The explanation is actually very simple, you should just read it! But basically they just generate variants of the word by deletions, not also insertions or substitutions. So increasing the "edit distance" multiplies the search space by n (the length of the word) instead of by n + an + a(n+1) (where a is the number of elements in the alphabet). Then there's cost in storing a larger dictionary of words, but lookup being logarithmic or better means that this should be fine. So yes, it scales better (at a memory cost).