When I click on the launcher I get the option to choose Diablo, or Diablo Classic. I have updated the DEP settings, which enabled me to run the Diablo Classic, but I wanted to try running the game with their updated high-resolution support. But as soon as I click the new Diablo option, the game just closes.

Does anyone have any idea what I need to do to make this work? I don't think a game installed straight from a loader like this should be difficult to run.

I'm having this same issue and have done what you did as well. CLassic works fine but the "enhanced resolution version" crashes as soon as i launch it

You might want to try DevilutionX, it has full upscaled resolution without most of the compatibility issues.
https://github.com/diasurgical/devilutionX/releases