I was wondering this same thing as a possible cognate with the German laufe which can mean either--but in German, means either to walk briskly or run, more often than not--at least in the Duo course offered. If I have erred, someone please let me know so I can correct this misconception.
Are you native english speaker? i'm not, but i was teached that questions in english require 'do/does' as auxiliar verb, or another verb such as 'will'. I believe that your construction ''they walk?'' is informal english, not predicted by grammar, but then again, i don't know.
Indeed it is a cognate of laufen. But it cannot be both run and walk. In Belgium lopen only means to run, in the Netherlands it only means to walk. And take care lopen is not used as extensively as in German es lauft or English it runs/things run smoothly to refer to how things are going (although in Belgium you can come across dat marcheert).