You will be able to get the result you want, but the setup is a little unusual. GameEx is geared towards setting up emulators that run games via command line functionality (which most do)...but every so often someone asks how to set up a game list of stand alone PC games. This is the type of setup you will need, but it is very doable as long as each game has it's own executable.
First of all, I suggest you go with the regular GameEx as it is much more configurable than GameEx Arcade.
Create shortcuts to each game executable. Each one will need to be named differently. If they are the same, that adds some complexity. Stop and let me know if that is the case.
Set the names of the links to whatever you want displayed in the game list.
Place the links in a folder outside GameEx. Let's use C:\ArcadeProject\Links as an example.
Next, run the Setup Wizard.
The sections you will need to use are the Emulator Setup and Enable/Disable Features. Use the quick links on the left sidebar to get to them.
In the Emulator Setup, we need to set up a sort of faux emulator. Choose an emulator number (probably #1 in your case).
Set the Start Page Name to something cool.
Set the Title Text to the same cool name.
Set the Working Path to the main folder: C:\ArcadeProject
Set the ROM Path to the shortcut folder: C:\ArcadeProject\Links
Set the Rom Filter to *.lnk
Set the Command Line to "[ROMPATH]\[ROMFILE]"
Lastly, I suggest setting Enable/Disable Features > Fix to Emulator to your Emulator #. This will make GameEx load directly to your student's game list so you don't need to navigate to it manually.
For a basic setup, that is it. It should do what you want.
But I am thinking that you might want to fancy things up once it is running...so extra credit time...
There are a ton of themes that can be downloaded. Pull a few down using the Download Theme option and choose a theme in the Theme section.
Be aware that most downloadable themes assume you have accompanying graphic assets such as in-game Snap shots, in-game Title shots, etc. Also, some are made for specific resolutions (or screen ratio, 16x9, 16x10, etc). So choose one that works for the assets and size you intend to have. Besides the default theme, A few I think might work for you are Default - Ultimate 1 or Default - Brokeh. They both look nice and only require Snaps and Title shots.
If you want to use Snapshots, set up a snap folder like C:\ArcadeProject\Snaps and place your snaps there. Then in the Emulator Setup, set the Image Snap Path to C:\ArcadeProject\Snaps. Both .png and .jpg are supported. Make sure the filename of the snap is the same as the filename of the game's link file. That is how GameEx matches the pics to the game. You can do the same for Title snaps, just create a separate folder like C:\ArcadeProject\Title.
If you ever decide to do video snaps instead, that can be done. The setup is very similar, but keep the video file sizes down or you might see a small amount of 'lag' when moving through the game list (depending on the rig you have inside the cabinet).
Also, there is an option called Display Settings > Hide Desktop that will show a black screen instead of the desktop while the game is loading. You may want to enable that once you are done for a bit more finish.
Good luck with it. It sounds like a fantastic idea. Feel free to come back with questions if you need to...and if you do go through with the project, it would be cool to see a snap of the cabinet running GameEx once you have it done.