It is control line, but with one line. Rather than two lines actuating a bellcrank via the regular handle, the monoline unit spins the wire CW or CCW of "center". The mechanism on the aircraft converts this to fore aft motion to the elevator pushrod. One line, elevator control. The thing with monoline is that the system does not lend itself to quick maneuvering, but for speed the rules is minimal control input, more like flying on the trims and holding a nice level smooth course for efficiency.
Airbusdrvr - sounds like you are describing the Mike Hoyt Sidewinder, or a similar model. Here is a recent version of the asymmetric approach:
http://flyinglines.org/kb.tarfu.html . These are flown by the pilot, not just attached to a post. The pilot generally holds the handle free of the center pylon, and assists line tension on his/her feet until the model gets up some speed and is trimmed out, then hooks into the center pylon for the speed run. This ensures the radius of the circle is consistent and prevents "whipping" by the pilot, i.e. helping the mode along.
I've said this before on other threads, but don't think the wings are there for looks only, they do provide lift. But you don't need much wing at these speeds. Asymmetric designs with longer inside wings or only inside wings, benefit by covering a greater % of the line/lines - which are very draggy at speed.
Speed flying is a very technical pursuit, requiring far more in-depth engine knowledge than many other competition classes. Some people poo-poo it as not really flying, but that's not fair IMHO. It is a specialized form of flying, indeed, and is an event for the type of competitor who relishes the technical details that harvest every last mph out of a system. I've always found it very interesting.