The purpose of an IFR flight plan is to tell the controllers where the plane wants to fly. Once the pilots start talking to the ATC and get their initial clearance, the routing can be amended any time by ATC, whether on pilot request or for other operational reasons, and this is just coordinated among the controllers and entered in their system.
An engine failure is an emergency, so the controller will mark the aircraft as having an emergency in the system, and might update the destination in the system. But even for diversions that are not emergency, the controller just updates the data in the system. No need to involve the dispatcher. Even if it is actually the dispatcher requesting the diversion—sometimes something fails on the airplane that allows it to fly on, but because fixing it in the original destination would be difficult, the dispatcher asks the plane to return to base or another hub and arranges different plane to complete the flight—but they still don't file another flight plan, just tell the pilots to request return to base and pilots handle it with ATC.