What happens if the vampire is knocked unconscious and then the resident tells another person to bring them inside?

The another person can freely drag the vampire into the house. The vampire is not entering the house, he is being entered into it which is a different act.

In your hypothetical scenario, if vampires were to somehow gain control of the government, could they simply pass a law stating all vampires are invited in all domiciles?

Yes, but it wouldn't have the effect you expected because the people still living on those homes have not invited them in.

Invitations are not associative and not transitive. If I invite John to my enter house, that doesn't allow James to "infer" that he's also invited, nor does it allow John to invite James into my house.

Answering to the question as posed, and supplementing somewhat on @Zonetrooper 's answer, for the purposes of worldbuilding "dragon" ends where your audience believes you made it end.

Yeah, like that's so helpful. But I feel that's kind of the point. In Neverending Story, the story and characters are presented in a way that we are willing to believe Falkor is a dragon, we don't need much more argument on the subject.

Monster Hunter has what IMO is one of the most interesting takes on the subject, with people having their own little in-universe arguments about what even counts as a dragon and why versus the more general surrounding concept of "wyvern" — yet, all in all, we are willing to believe that the people in the MH world are willing to believe that Kirin, a thunder pony, is a dragon, much as a giant graveyard squid is also a dragon. So we can have fish dragons, jellyfish dragons, amphibian dragons certainly, if we believe that there's enough intrinsic weirdness to them to make them dragons.