I suggest giving a try to devilutionX instead of WINE, I expect it to work flawlessly. But I’m not sure it supports Hellfire yet.

On Ubuntu you can use ./play.it to generate .deb packages from your GOG installers, that will in turn use devilutionX to run the game. Once installed, it should be as simple to use as clicking the "Diablo" shortcut in your applications menu.

I have the same problem.
There are basically two options in the launchers list right now from what I can see:

1) LINUX GOG + DevilutionX Linux x64 version last published 2 months, 3 weeks ago
This works for me but it only supports the base Diablo game, the Hellfire addon will just be ignored.

2) WINE GOG - Hellfire - Vanilla version last published 1 year ago
This one CLAIMS that it supports the Diablo+Hellfire combo version specifically from GoG, but it doesn't work! After playing the intro movies of whatever you try to start the game will just terminate back to desktop.
Which is weird.. considering it specifically says "The GOG version of Diablo, with both the classic option and Hellfire expansion working." so I wonder what the author didn't take into account here?

hellfire is almost finished so expect it to be available soon ;)

Next devilutionX release maybe? ;P

I've never played Hellfire despite Diablo being one of my first video games, so I'm really happy to think I will soon be able to give it a try.

Yeah, it's just a few weeks away at this point.

Hey just letting you know that DevilutionX 1.2.1 is now available with full Hellfire support :)

https://github.com/diasurgical/devilutionX/releases