I noticed when trying to install the GOG version of Streets of Rage IV that the default script seems to grab the the windows version and run it through WINE, even though there is a Linux version available. (It also doesn’t seem to work in WINE)
FWIW the Heroic Games Launcher grabs the Linux version, and that runs fine.
Well the scripts are intended to help specific versions to work, in the installer scripts there are a Wine and Steam version. If you can or want, you could create a installer for the Linux version but I suspect it is just easier to install it directly to the system and then add it to Lutris with a launcher.