The show was being recorded at Chubbuck's specific request - her family believe that she did so because she expected the footage to be shown around the country.
No-one seems to recall who the guest was - could have been a local official of some sort, business person, teacher, who knows?
U-matic (or BVU) cassette machines were also around at that time, although I couldn't say whether WXLT had one. They'd certainly be a vastly more viable option for recording the show for a guest - the original tape would be a 2" quadruplex reel, which would only be replayable on TV station equipment (the machines were the size of a large refrigerator). From that original, the station could have dubbed a copy onto a U-matic tape for the guest, who may have had access to a machine (after all, why ask for a copy if you don't have the means of playing it?).
BUT... as the guest didn't actually appear (Chubbuck shot herself at the start, and the rest of the show was abandoned), I doubt that a copy would have been made for him / her by WXLT. It's at least possible that a copy may have been made for the FCC, but I can't remember ever seeing any reference to one (which doesn't mean it didn't happen, of course!).
Problem with videotapes - of all types, but especially 2" quad and U-matic - is that they deteriorate; transferring them can be very difficult, as many need to be baked before being able to be used. Even if the original 2" reel exists, and the family decided to make it available (which I can't see happening after all this time), the footage may not be recoverable...
It
does sound as if the author of this piece saw the video:
http://www.manship2.lsu.edu/perkins/...hubbucknew.pdf