It's a wonderful word. It acknowledges that engineers and artists are yoked in the same enterprise. The word machine is similarly rooted in the arts. An unexpected god steps out of a clever stage machine to save a hero at the last second. A fairy godmother appears in a puff of smoke to pay the mortgage.
Science comes from the Latin word scienta, which means knowledge.
And engine, like engineer, comes from the Latin word, ingeniare. However, engine is one word whose meaning has changed. It used to mean any product of the mind or innate mental power. Today it usually means a physical machine, although the original meaning is sometimes still applied. In computers, a search engine is software that seeks out information.