Wether Steam Powered Or I.C matters Little, a "Donkey Engine" was a small(ish) engine used to augment manual tasks on board ship, and as such the operater was said to be donkey riding, when at work. incidentally there are quite small steam engines that would fit easily onboard ships.

Just to avoid confusion, I am not the "henryp", who also sometimes posts here !! hence the use of the geographical location above..