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Remnants of the Precursors resembles Stars!, but Stars! doesn't seem to much resemble Master of Orion 1 or 2. Seems to be convergent evolution. If I recall correctly, there were many similar 4X in space games at the time, and Master of Orion 1 didn't stand out much - it was Master of Orion II that was a big hit, relatively speaking (4X in space were/are a bit niche).

I can't speak for the authors' mindsets, but the Stars! map had pointwise movement rather than via strict stellar/planetary waypoints. When fleet interceptions can happen midcourse[1], there's not a whole lot of design room within the Win16 style.

[1] — If I remember correctly, there even was some special-case code for ship pursuit cycles.