Have you tried reinstalling, yet?

On a side note, make sure you're installing the game outside of Program Files.

Or you could install it with Galaxy, which will keep the game updated, when they release patches (like in Diablo I).

Whatever the case, good luck.

Edit:
Here's a page that describes some fixes, perhaps it will help

https://pcgamingwiki.com/wiki/Warcraft_II%3A_Battle.net_Edition#Issues_fixed

You might have realized by now, but I'll just mention it anyway.

For some reason I can't get the installer to make a shortcut, so I have to make my own.

Using 'War2Launcher' gives that error when I start it the same as OP says, use 'Warcraft II BNE_dx' instead and it should launch fine.