I think zügig probably comes from the other, older meaning of Zug, "pull", "drag".

Zug does mean train but it comes from ziehen (to pull) as others mentioned. So I am not sure whether zügig comes from the original meaning or from 'train'. The english cognate for Zug/ziehen is tug btw (follows the common t -> z shift in german)

Confirmed. I think, “steady” is a good rendering.

Not quite. "Steady" usually implies a certain slowness. "Zügig" generally implies the opposite.

For example, if I asked you to leave a hotel in a "zügig" manner, I would be asking you to quickly pack up your things and then leave. In other words, it's about doing something "faster than normal", but not so fast you can't take proper care.

If I told you to leave "zügig" and you'd first finish watching a TV show, I would probably be slightly irritated.

In this case "zügig" is better translated as "in a timely manner" (rather than with haste, which would imply dropping what you are doing and running away).

In every explanation of the word 'zügig' here on HN, the word that pops into my head is 'directly'. Not sure how to make that work beside the word 'programming' but it matches the same concept.

It implies that you are following that one named goal and considering nothing else.