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.
This was fixed already, but a new release of Lutris has not been published with the fix included. The exact line in your screenshot was specifically removed in this commit:
https://github.com/lutris/lutris/commit/3b64e70e2a2a4f90e2679b12f9f2bf56cb0a5986
Good to know. 👍