Can someone explain how this RFI filter works?
Brushed DC motors can produce quite spiky commutation current so I expect the filter is to stop excessive noise getting from the motor and onto the 12 VDC power supply. The inductors and capacitor (together) form a 2nd order low pass filter. 

It's difficult to say anything more without an in-depth motor analysis but If you are trying to replace the 2.2 uF polyester capacitor it's best to try and find something as close as possible. I could make guesses here and there but these are not warranted because the number of capacitors of this type that are available is staggering.

17x 2.2 uF 63 volt film capacitors on Farnell for instance

Changing the capacitor to 1 uF will increase the cut-off frequency from about 51 kHz to about 76 kHz. This may still be OK but it's not for me to say.