Are four-engined airplanes subject to ETOPS equivalent rules?
Yes, three- and four-engine airliners follow 'Long-Range Operations' restrictions just like twin-engine airliners.
From WikiPedia:

Airbus proposed to replace ETOPS by a newer system, referred to as LROPS or Long Range Operational Performance Standards, which would affect all civil airliners, not just those with a twin-engine configuration
(...)
The FAA has decided to use the single term, 'extended operations,' or ETOPS, for all affected operations regardless of the number of engines on the airplane.

The large 4-engined airliners can not reliably fly long distances on one engine only.  But  they can fly on three engines just fine.  When only two engines are available they divert to the nearest airport.
The ETOPS rules become relevant whenever a three- or four-engined jet diverts more than 180 minutes from the nearest airport.
For more information, refer to the airliners.net thread on 3 And 4 Engine Planes Requiring Etops.