Just to clarify a point that seems confused in the article MP linked to, the "Star Trek Magazine" article on designing the original Enterprise (
http://www.starfleetcom.net/lcars/fsd/art/1701.html) makes it clear, per Mr. Jefferies himself, that this ship does originally date from the early days of TOS. Also, in the Magazine article on the Vulcan cruiser from "Enterprise" (
http://www.starfleetcom.net/lcars/fsd/art/timur.html), Doug Drexler talks about taking his inspiration from this veyr design--a nice bit of Trek continuity in a show almost entirely lacking in it.
As to what the heck this ship is supposed to be, it seems that nobody knows--
from Rick Sternbach via Ex Astris:
My only exposure to that design was back in 1978 when I was on ST:TMP. The script called for a few ships called Enterprise to be exhibited in the Rec Room. Gene Roddenberry asked me to stop by his office, where he gave me a copy of the painting of the ship, printed as a poster. He asked me to make that design one of the five or so ships in the Rec Room alcove. So who was I to say no? ... As to how that ship fits into Trek history, I really don't have anything intelligent to say. I don't know much about it, never speculated about uh, specs, and have no real opinion about whether it was a civvie vessel or a Federation vessel or just what it was. I also have no additional drawings or even the poster I worked from in 1978. You'll all have to carry on as best you can to shoehorn it into the lore.
The obvious speculation, with the ENT Vulcan cruisers now in the equation, is that this an attempt by human designers to recreate the "ring" warp drive system that the Vulcans use. It would seem to follow that the attempt was not particularly successful, as this is the one time it seems to ever have been tried...
Nice work, Azel--especially from the DVD and memory alone!