The filter boards may also be in place in order to reduce the amount of electromagnetic noise that's radiated by the cabinet. These cabinets do have a certain emissions standard that they have to meet, and one of the ways to put a lid on emissions from a line is to run it through an inductor (basically, a metal ring with a wire wrapped around it. See the wikipedia article on inductors).
The idea is that the inductor (if kept small enough in value) will sort of take the edge off the signals (round out the square waves, slow the transitions ever so slightly). This will change the EM signature of the whole mess, hopefully making one meet whatever standards are applicable.
Putting them on a separate board has advantages in that you don't have to re-spin your main PCB, so you can get to production sooner.
The filter board was placed there in order to try to fix some issue. Whether it succeeds or not is an interesting question, but it definitely adds one more point of failure, and some folks recommend removing them for certain games. Unless you have a reason to do so (like your board is flaky, or the game is widely known to have problems with the filter board) I'd leave it in place.