Your settings are stored in your browser’s local storage. If you delete it, your settings are gone. You can whitelist local storage for online-go.com to keep settings.
Please note that deleting cookies doesn’t do much for your security. The only site being able to read your cookies is the site which created it. Also deleting session cookies doesn’t make them invalid. An attacker who has acquired your session cookies can use them even after you deleted them.
The little privacy you can get by deleting cookies doesn’t work for 1st party cookies of sites you login. At the moment you login, you are identified to the site anyways. Considering this, you can create an exception for online-go.com without decreasing your security and privacy level.