It's quicksort for linked lists.
Yup, this is quicksort, just not in-place. It matches the high-level algorithm for quicksort whilst changing the low-level implementation to match the data structure of linked lists. That's why it's quicksort for linked lists.
I'd prefer to say "quicksort was originally developed to work in-place" than "true quicksort is done in-place". There are many variants of quicksort including picking pivots randomly to avoid worse-case behaviour etc.. This is a sensible, clear definition of quicksort for linked lists.
This definition exactly matches how we teach quicksort to 16 year-old maths students in the UK. (We're teaching algorithms, not programming.) In-place very much obscures the purpose and design, which is why we don't teach that detail, despite being a million miles from teaching functional programming or linked lists. (That doesn't change the fact that the pair-swapping trick in-place algorithm is best when you have destructive update arrays.)
There is a time penalty to this definition, since it traverses the list twice for the two sublists. It's certainly possible to rewrite this to partition rather than filter, but I assert that that's optimising rather than changing the fundamental algorithm here, quicksort.
