You can try to install EVE the normal way, meaning, you use a recent WINE version (3.0 or later) and install the Windows client for EVE.
This is working and only requires you to set WINE to “Windows XP”-mode through winecfg. Then you can run the Windows installer and play the game just as you would under Windows.
And do make sure that after the upgrade of Ubuntu you still have access to the 32-bit packages. If not then you’ll have to do the following again:
dpkg --add-architecture i386
and install wine32 (or wine32-development if you rather prefer those) and not only wine or wine64.