I haven't watched that anime yet. I also never even came close to the real thing.
What I do know is that one popular picture of the black X68k alongside a matching monitor and keyboard are to me the embodiment of the cool industrial/utilitarian late 80s computer design. The computer tower case looks like some premium stackable industrial equipment. The only thing I can think of that achieves similar iconic level is the PowerMac G5 "cheese grate" tower.
In the first episode of Battle Programmer Shirase, a representative of "Eibin Corporation" comes to the title character asking for help with a cyberterrorist who is holding their company hostage and demanding that they bring back their "EX68" computer line (to which Shirase replies that he wishes that they would bring it back too). Note that "eibin" means "sharpness" in Japanese. That's the X68000's reputation, to the point that it warrants nerdy references in anime decades after the system's heyday.