I'm hoping for a game that is fully developed in terms of gameplay, but not visually realized.

How the visuals of the game affect the mechanics of the game.

This is sort of the "you can't have your cake and eat it too" sort of dilemma. Visual themes play a huge part in how games are designed and how mechanics work. It's going to be almost impossible to find a game that isn't basically fully realized thematically and visually.

I would try to find board games that are "bundles" of unique games that can be played in the same box. Many of these games have more generic and basic game pieces/boards because they have to be used for many different games. If you sort of like chopped up these games your students could then fully design and flesh out the visuals for their game pieces/board/box/etc as a solo product sort of thing. An example that comes to mind is "Pyramid Arcade" which has like almost two dozen unique games that mostly use very basic boards and tiny plastic pyramids, which could easily be rethemed and given their own stories.