The unity project seems to run out of the box on Linux after installing a certain libssl version on my Linux Mint machine.
wget http://security.ubuntu.com/ubuntu/pool/main/o/openssl1.0/libssl1.0.0_1.0.2n-1ubuntu5.10_amd64.deb
sudo dpkg -i libssl1.0.0_1.0.2n-1ubuntu5.10_amd64.deb
I can run the game in preview mode. It connects, I can select cards, pets and click the play button which makes the game wait for other players. (of which there are obviously none currently)
Nice project. Unfortunately I have 0 experience using the Unity engine so I won't be able to help much. But if you need a Linux tester just message me.