The official launcher, which is what downloads the actual game, will not run on plain Wine. It does launch under Lutris or Steam when added as a non-Steam game with Steam Play compatibility enabled. However, it appears to be broken and it will be stuck at 0% download progress. If this somehow works for you, consider this guide outdated.

It is possible to run the game in Wine once you obtain the files. To do this, you'll need to generate a signed, temporary download URL, just like the game launcher does. You can replicate it by running this python script. Note that the MJS server sometimes returns invalid links for some reason. If that happens, try running the script again in 10 minutes and it usually works.

Download the zip file link it printed out, unzip and launch in Wine. No extra setup should be necessary (at least on Wine 8.3 or later).