I’m not a fan of Kimbra’s "Good Intent" in and of itself, but the music is appealing.
Can anyone tell me what that style of music is called?
Wiki calls Kimbra’s general style “jazz influenced electropop”.
Tricky sort of category. Thanks, Richard Pearse. 
While I’m at it, does know what the beat style is called, from a dancing perspective?
I wouldn’t know what to call it in terms of dance, but from a purely musical perspective it seems to be a fairly straight forward 4/4 rock beat (perhaps 2/4). There’s no shuffle/swing/triplet feel or anything. I think a lot of the quirky feel the song has comes from the rhythm of the melody, the syncopation of the bass line (playing on the off beats), and the choice of instruments.
Many thanks