From AB's Getting to Grips with A/C Performance:
“JAR/FAR 1.1: 'Critical Engine' means the engine whose failure would most adversely affect the performance or handling qualities of an aircraft”, i.e. an outer engine on a four engine aircraft.
There are 26 instances of "critical engine" in that document, all of them being paste-copy quotes of regulations. Not a single mention that there is actually such thing, except from the very one I quoted above.