A good definition of Engine should also include bad ones. This seems dumb, but a deck doesn't have to be successful to be considered an engine. It can be bad and an engine, it's just a bad engine.
I think of an Engine as a deck that tries to play lots of cards. Usually actions, but some engines are built to draw money by playing lots of draw cards, and some engines have alt-treasure or alt-VP components, so I wouldn't exclude them either. Just, lots of cards. Lots of them. So many cards.
So, I define "Engine-ness" as the fraction of your deck that you expect to see on a turn, on average. You will note this is not binary, it's a spectrum. I think that's a good thing. (N.B. this directly corresponds with "how often does this deck reshuffle." This definition is less intuitive, but easier to calculate from game logs.)
As a benchmark, take a boring BM+X deck. It probably buys one card a turn, so on turn 15 it's got 25 cards. If it just plays money, it sees 5 cards, for an Engine-ness of 20%. If it plays a Smithy, it sees 8, for 32%. On average, a BM+Smithy deck gets an engine-ness of <30%. So we'll say an Engine has to beat that considerably.
On the other end, a deck that draws itself has an engine-ness of 100%. In fact, it's technically possible to get over 100% through heavy use of sifting cards, like a Minion deck that cycles itself more than once--I consider a card "seen" if it passes through your hand, even if you don't play it. We would call this an engine, even if it's not doing anything useful. It's not a good engine unless it's hitting at least $8, but it's still an engine. (A deck of 0 cards shall be christened "the trivial engine.")
And now let's take a look at cards that score in the mid-range, around 50%. One way to do this is with a deck with 20 cards, that goes through 10 cards a turn. This would describe a deck that on turn 15 has bought one card per turn, has trashed half its starting cards, and expects to play two villages, one smithy, and probably one or two more non-drawing terminals. That sounds middling-ly enginerific to me. Another deck that scores a 50% is one that is similarly 20 cards, and plays 5 cantrips per turn plus a terminal. That's an ok-not-great Conspiracy engine.
Either of these decks could edge up their engine-ness to 60-70% by trashing 3-5 more cards, or by gaining 5-ish cantrips, or by gaining two warehouses to sift through more of their deck. These activities are generally considered to be part of playing an engine, and possibly defining it.