I don't take the "Enterprise Class simulator" sign in TWOK too seriously. After all, despite the inclinations of some fans to pretend that this is some consistent reality where every detail is equally binding, the fact is this is a bunch of different works of fiction invented by different people who interpret things in different ways and sometimes just make mistakes or forget stuff. So if most episodes/movies say one thing and a single instance contradicts them, it's often best just to dismiss it as a continuity glitch.
Besides, it was a simulator at a school, so maybe it was "Enterprise class" like "history class" or "shop class."![]()
Or Enterprise Class as in the class of cadets that are currently assigned to the Enterprise is currently in the simulator.