Well, strictly speaking for dramatic purposes there's no reason why the engine room couldn't simply be a control room tucked between the nacelle pylons next to a transformer or circuit breaker that brings ship's power down from the nacelles to the rest of the ship. In point of fact, most engineering decisions on modern naval vessels are made in the maneuver room or the motor room, not the room where the actual power plant (or reactor on a nuke boat) really are.
On the other hand, the same can be said for the TMP Enterprise. Arguably, the intermix chamber was just a power transfer conduit with the reactor room far below decks, so "Engine Room" in the refit Constitution refit could be anywhere you need it to be.
That gives me a thought. Suppose the warp reactors of the TOS ship really was in the engine nacelles? In that case the gigantic machinery bay on the other side of the chainlink fence might just be a massive energizer array where drive plasma is siphoned downwards from the warp nacelles and then converted into energy.
On the other hand, the same could be said for the TMP Enterprise. There's certainly nothing in canon that suggests the intermix chamber MUST feed towards the nacelles and not the other way around. It's entirely possible the drive plasma is produced in the warp nacelles (where the bussard collectors are) and channeled down to the so-called "Engine Room" where it's converted to electrical energy or channeled into the impulse engines high above or the main deflector far below.
The only thing that doesn't fit this theory is 24th century technology, but then there's no reason to assume the 24th century equivalent isn't vastly more advanced than the engine designs of a century earlier, appearances aside (like the difference between a piston-driven aircraft and its jet-powered counterpart).