As the title suggests, Lutris is requiring me to sign in to GOG so that it can verify my ownership of the game. If my memory serves me well, I used to be able to simply click on the GOG version and then link it to the installation executable file that I downloaded from gog-games.com.
You are not logged in. However you can subscribe from another Fediverse account, for example Lemmy or Mastodon. To do this, paste the following into the search field of your instance: !piracy@lemmy.dbzer0.com
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Use the Lutris website to find the game and install script, that should bypass the login check and let you bring your own exe.