Question

In cooling of the engine, extended surfaces are used in the water cooled engine.

Answer 1

Because the engine you describe is NOT an oil cooled engine as such. It is an air cooled engine.

First oil is always cooling any kind of car engine. That means you could call all engines an oil cooled engine but that is not the primary purpose of the oil. That is the secondary job of the oil. The fins are there to help carry the heat away from the engine. Usually there is some kind of Blower as well. Old VW air cooled engines come to mind as a prime example. This is not to say an engine could not be built that was purely cooled by oil. It is possible though I don’t know of any.