My guess, although due to my move my copy is already in Bangor so I can't check, is that Barlow's campaign of feeding on the town was already well under way by the time he entered that house. We had already seen the Petries dead son in an earlier scene asking to be let in. His brother did not do so but that doesn't mean he hadn't been dining on the parents. The method used by the Lot's vampires was to enter and feed off the living for several nights (to stretch the meal) and said people slowly got weaker until they died.
What this most likely means is that the dead Petrie had already been invited into the house by one (or both) of the parents. By extension, perhaps Barlow can enter any place his minions can enter. He is the King Vampire after all. Of course, I don't recall there being a huge deal being made out of the "invite" part of the legend, at least nothing sticks out boldly in memory. Vampires in the various books by Sai King area often broken into types, and Barlow is most certainly one of the most powerful, i.e. one of the "Grandfathers" as Roland calls them. The strengths and weaknesses of the various types vary widely. The simplest answer, I think, is that the Grandfathers don't need an invitiation.