Is 'spazieren' the correct translation of walk in this case? I always thought it was used mostly in the context of 'spazieren gehen.' Or does it simply have a different connotation than 'gehen' or 'laufen' would?
'Einfach durch die Tür spazieren' is a fixed idiom, so you don't have much of a choice here, it's 'spazieren'.
I guess I was lucky, because DL accepted "gehen."