Sorting of integers and floats 23% faster in PostgreSQL 9.2 (long explanation)

Definitely not quick sort -- getting it to be an O(n log n) worst case is very hard, and usually enough to disqualify it as "quick" (if such a title is ever warranted, given the n^2 worst case).

Any reason why specifically radix sort, rather than (say) TimSort (super-optimized merge-sort), which has better memory locality than radix sort, and can accommodate non-lexicographic orders (useful for e.g. non-normalized unicode) unlike radix sort?

Only if you actually can special case it automatically during compilation. It could still require a few tricks if your comparison comes from a user-defined query. At a minimum it would have to be something like: figure out which column type are you using, figure out what basic type does it map to, use that type in the template.