Ok, so you already took care of the monitor orientation, cool.
Yep, any standard 15A switcher like that will do to power the jamma board.
Although how do you plan on actually tying in the power. The adapter you linked doesn't appear to have a means for that. Actually it looks like its meant to power it off the existing supply pins.
The 60-in-1 has a a molex jack on it, so if you were to disconnect the connection from the existing power unit, you can then use the molex connector to power the new 60-in-1 board
You can do this by hacking the connector off an old computer atx power supply and wiring it up to the new power unit for +5 volts and +12 volts.
Or you can just use an d computer power supply if you have one. You will just need to jump it out for it to power up.