Engines may be a relatively recent invention, but "engine" the word has been around for quite some time. Here, for example, is the poet John Gower using the word to describe women in the 14th century (emphasis added):
The craft Minerve of wolle fond
And made cloth hire oghne hond;
And Delbora made it of lyn:
Tho wommen were of great engyn.
Meaning, roughly (thanks to scholar Karl Steel for the assist with this):
Minerva invented weaving from wool
And made cloth of her own hand;
And Delbora made it of linen:
Those women were of great machines.
But no, of course not. A machine would have been entirely anachronistic (and not make very much sense). Engine, however, was not out of place at all, as the OED's Richard Holden explains. The word comes from the Latin ingenium, related to our own word, ingenious. In saying those women were of "great engyn," Gower was saying they were crafty or clever.
Over time, as we know, this abstract concept of inventiveness or cleverness came to refer to a complicated, powerful piece of machinery. This, Holden says, is a great example of something that is quite "common in English nouns: the transferral of what was once an abstract concept to something very concrete."
In his post, Holden explains that from the abstract concept of ingenuity "it was only a short step to applying engine to the products of ingenuity." He writes:
At first, these engines were relatively simple, and could include anything from smaller objects, such as bows, nets, or ropes, to larger ones, such as catapults or torture racks. This broad sense remains current in English only in isolated cases, such as in fire engine, which originally referred to any apparatus used to put out fires (including buckets, ladders, and ropes), and, oddly, in fishing contexts: "2002 Irish Times (Nexis) 20 Mar. 26 In its first year of operation, 13 owners of 23 fishing engines (nets and traps) have agreed to cease fishing on a permanent basis."
Beginning in the 16th century, Holden says, "engine" could have been applied to all sorts of "ingenious" machinery -- clocks, mills, pumps, and (later) the steam engine. This soon expanded: "These steam engines could be stationary ones, imparting motion to other machinery," Holden writes. "Or they could be given wheels and used to pull heavy goods, as in a locomotive engine or traction engine. They could also, most pertinently from a modern point of view, be fitted into a vehicle in order to make it move." The earliest example of this in the OED is from a magazine called Niles' Weekly Register, in which was written "I have lived to see boats succeed well with those engines."
By the middle of the 20th century, an engine was no longer an abstract idea of craftiness but a concrete manifestation of that craftiness: the engine, the machine that moved the world by car, plane, train, and boat.
Interestingly, the use of "engine" to describe these machines gave rise to another abstract meaning of the word: "anything considered a 'driving force' in some way, from ballerinas to football players to countries," writes Holden. He quotes an example from 1977: "The motive power is the music; the dancers are the engine whose output comprises some of the most weird, astonishing and beautifully simple ballets ever seen."
In more recent years engine has found new life once again: the search engine. Though these engines are digital, algorithmic, lacking in the mechanical quality of earlier engines, the word remains true to its earlier inversion. The search engine, along with the steam engine and the internal combustion engine before it, is the product of ingenuity, a manifestation (though not a physical one) of human labor and inventiveness. Perhaps if John Gower were here today he'd observe that like Minerva's wool and Delbora's linen, Google's search is of great engyn.