What is this pipe thread compound on my LP regulator fitting?
The tape you purchased is the correct tape for gas fittings.  However, the fitting in your picture is a flared fitting.  PTFE (Teflon) tape/pipe dope is only necessary on pipe thread fittings.

This is because pipe threads are tapered - as you tighten the fitting, the threads bind together and deform slightly to create a seal.  The pipe tape/dope helps lubricate the threads and make a better seal.

With a flared fitting like your photo shows, the flare at the bottom seats in a mating flare inside the female fitting.  The threads are only there to draw the two together.

Using tape on the flare fitting may not cause any problems, but I would not take the chance, especially with gas.  If any tape gets under the flare or prevents the nut from tightening down fully, you're going to have a leak.