Are run-ups required for multiengine piston aircraft?
Yes, From the FAA handbook 


  ...be operated from its crossfeed position during the run-up. The
  engines should be checked individually and allowed to run at moderate
  power (1,500 rpm minimum) for at least 1 minute to ensure that fuel
  flow can be established from the crossfeed source. Upon completion of
  the check, each engine should be operated for at least 1 minute at
  moderate power from the main (takeoff) fuel tanks to reconfirm fuel
  flow prior to takeoff.


And also 


  Some multiengine airplanes have a ramp weight, which is in excess of
  the maximum takeoff weight. The ramp weight is an allowance for fuel
  that would be burned during taxi and run-up, permitting a takeoff at
  full maximum takeoff weight.


For what its worth a multi-engine piston plane is mechanically double what a single engine plane is, and often carries a similar if not the same engine as a single. The things you are checking in run-up, primarily the ignition system holds true for both single and multi-engine aircraft.