On the other hand, it seems odd that a deck which draws itself every turn but still can only gain one VP card a turn is not an engine ("draw-your-deck money"?), but then you add a single source of +gain and suddenly it becomes an engine. So like a Scrying Pool one-terminal-per-turn deck with a single Expand as the only source of additional points (an example to reflect an actual game I played), and that stops becoming an engine if you remove the Expand?
So thinking about engine in contrast to money, we usually refer to money decks by a single card, e.g. Embassy-BM, Swindler-BM, etc. Even if there might be another kingdom card in the deck, that's not the focal card and doesn't interact with much with the focal card, like maybe there's a trasher that does its job early and then turns dead.
Extra gains don't generally turn a non-engine into an engine, or else we'd have to call a deck with a bunch of Silver, Gold and a few Margraves an engine (I'd call it Margrave-BM).
Nonterminal stacks are a gray area, especially lab variants. Like would we say "Hunting Party BM" or "Hunting Party engine?" I think that depends: usually I say the former if the deck consists mostly of HP and treasures, with maybe one other terminal. But if I'm using HP to draw villages and terminals and play them, that's an engine.
So I think the defining feature of engines is interaction. A money deck has one action as its focal point (maybe two, depending on how we classify Lab-variant-plus-terminal), and mostly uses that card for its effect in isolation. In contrast an engine is built around interactions between different actions.