It sounds like an admonition to me. A girl is complaining to her boyfriend: "Why don't you invite me round?" invite someone round = invite the round to your place Or it could b a suggestion. The girl really wants to go to the guy's place.

For me it is a kind of complaining. The meanings could be: - Why don't me invite me to a dinner/ lunch? - Why don't you take me out? - Why don't you let me visit your place/ parents....? Mostly this can be the complaint of a girl.