Yes, Robbie was playing a Gibson. Gibson made harp guitars in the early part of this century, as did some other makers. I've played them -- it's kind of like trying to hold a piano in your lap, and a lot of them don't sound that great, due in part to their heavy construction. But sometimes you can do some pretty neat things with them. The "harp" part is generally for one-note bass strings (with no frets under them to raise the pitch), basically to add fullness to the low end.

As for classical guitars (mentioned by Grab), there have been a number of experiments with these, too. Probably the most famous proponent was the late Narciso Yepes, a true classical guitar master who played a ten-string. For the most part, the "extra" strings were intended to be played as unfretted bass strings, like on the Gibson harp guitar. But there were frets under them (very wide neck), and occasionally I think they were fretted.