THIS exists in M-E?

[HerenIstarion]

Legate of Amon Lanc

Though personally being in favour of 'Translator's Conceit' idea, I'll feed you some other idea if you really need to have railways in Middle-Earth...

HoME, Volume V, II. THE FALL OF NUMENOR.

The old line of the lands remained as a plain of air upon which only the Gods could walk, and the Eldar who faded as Men usurped the sun. But many of the Numenorie could see it or faintly see it; and tried to devise ships to sail on it. But they achieved only ships that would sail in Wilwa or lower air

Ibid, LOST ROAD. Chapter II, Alboin and Audoin

The world is not a machine that makes other machines after the fashion of Sauron

So you may consider words 'express-train' and 'engine' (this latter when it refers to a train, not engine in general, I suppose) not as things new and only known in the Shire, but as legends/rumours/memory of things that were, or might have been in Númenor, devised either by Númenoreans themselves (as ships to fly the air) or by Sauron (machines making machines. I, Saurobot, made these... ). Probably Sauron, unless they've used coal - just in his line, to cut trees and burn them to make a thing made of iron move