I don't think these interviewers expect quicksort verbatim (though they usually don't ask for a run-of-the-mill algorithm).
They want to see your thought process as you tackle an unfamiliar problem. Do you think about the input and the end-goals explicitly? Do you consider multiple different ways of solving it, and cover pros/cons? Do you consider where issues may occur, and attempt to mitigate them? That's what they want to see.