In the case of games like X-Wing, I can understand why they stated 386 minimum - trying to play that on a 286 is an exercise in frustration, and they probably just wanted to minimise the complaints from AT owners who would have gotten a horrible experience.
Whilst there are plenty of 286 owners here with hot rod systems that can easily give low-end 386 systems a run for their money (or even comprehensively beat them), that wasn't the case back when X-Wing came out - the majority of 286 systems would have been relatively standard 12 or 16MHz jobs with basic, slow VGA cards.... and really not up to the task.
There's technical specifications and marketing specifications intended to make the publishers helplines/forums/BBS a little easier!
Of course it makes tracking down definitive answers 30+ years later a little tricky when the specs on the box/manual/website doesn't actually reflect the reality!
My collection database and technical wiki:
https://www.target-earth.net