Sorry, I should have looked this up first rather than being lazy and asking everyone else.
It appears that there was a 2-player co-op only arcade machine (and it was in fact missing the "tournament" moniker). Here's a link to one that is for sale:
http://www.quarterarcade.com/Game.aspx/4157My guess is that the developers started with the ROM for this game (which is different than the ROM for the 4 player version), emulated it, and then added xBox live capabilities (which would explain the lack of head-to-head of any kind).
... I just hope that by some miracle someone decides to make an updated version of the game. But my worry is that there are only 2 real possibilities:
Game sells well - and the lesson learned is "see, we didn't need head-to-head to make money"
Game sells poorly - and the lesson learned is "there is no money to be had with this franchise, don't bother making an updated version with head-to-head coolness"
Hopefully I'm just being a debbie-downer, as I'd really love to play a version with 2-on-2 and other goodies.