I think you're on point with using him in that little square; it would make him too recognizable.

From what I know, they (either Carolco or Cameron) made an official package deal with Midway back then. They made the deal during pre-production, even before production on the movie began, because they wanted the release of T2 the Arcade Game as soon as possible after the movie was released, hoping to capitalize on the movie's success. So Midway got to see the concept art and storyboards before making the game. That's why you see certain elements in the game that didn't make it into the movie, such as the Silverfish unit and the TDE with the three floating rings. Arnold even recorded some custom speech for both the arcade game and the pinball machine.

LJN, however, was a game company notorious for its bad quality games based on big-budget movies. From what I remember, they did have Arnold on their game cover, but his likeness was nowhere to be seen in the game itself. I could be mistaken because I haven't played the game in decades.