It's important to understand is that these games you are playing in MAME™ are not PC remakes of classics, they are the real arcade games being emulated on your PC. So if the game only had one set of controls that you took turns playing at the arcade, the emulation software cannot change that. Games that had 2-player simultaneous play will let you do so on the X-Arcade™.
You can however simply reprogram the 2nd player side's controls to the exact same buttons as the 1st player side for these games, and then you could use either side for playing. Keep in mind that the person not playing could interfere with the other's turn.