It's pretty simple, just follow these steps.
I suggest a sanity check 1st. While running your theme in Reaper, run the theme tweaker script. At the bottom of the window, it shows the location of your theme image/resource folder.
1. Grab your theme resource folder. I suggest copying it to a clean folder.
2. Grab your theme's *.ReaperTheme configuration file. While in the theme tweak window, I would suggest clicking on the "SAVE THEME" button and saving a copy to the same folder you copied the theme resource folder to. Not inside the resource folder but in the same directory as the resource folder.
3. Now you should have both parts you need in a single folder by themselves if you followed my suggestions as described.
4. ZIP the resource folder and the *.ReaperTheme file into the same zip archive (I suggest using 7-zip to do this).
5. You should now have a MY_THEME_NAME.ZIP single zip file.
6. Rename that file including changing its .zip file extension to MY_THEME_NAME.ReaperThemeZip
Drag and drop that file into Reaper while it is launched as a sanity check to confirm everything works and it loads in Reaper and shows up as an additional Reaper theme selection menu item.
If all went well, then send that single MY_THEME_NAME.ReaperThemeZip file to your students and tell them to just drag and drop that file onto Reaper when it is running. Reaper will do the rest for them.
If it still doesn't work for them. Fail that student for not following instructions since you already verified it works.
If you would like an additional sanity check, then upload your MY_THEME_NAME.ReaperThemeZip file and provide a link for download on this forum and one of us can download it and additionally confirm if it works or not and explain to you what is wrong if it doesn't.