There are a few problems with this...
I'm not sure how youd get Windows to launch two full screen applications at the same time on two different monitors.
Configuring the second mame's controls is easy, but if player 2 inserts a coin and presses start to play pacman, and player 1 is playing tmnt, suddenly p2's character will become active and start moving around, preventing p1 from advancing.
Also, sound would be an issue...you would either have audio from only the first one launched, or both of them at the same time, which would be annoying.
You would be better off using two computers. The second side could be on a kvm switch to switch between a mirrored screen of pc1 and pc2. Depending on the encoder you used, the kvm should be able to switch the controls between both computers as well.