Playing needs the cookie
You denied the cookie, so here is the whole of what it is — and why there is no game without it.
Every cookie CardsLib sets is its own: written by this site, kept on its own servers, restricted to this site, and read by nobody else. There is no external tracking whatsoever — no analytics, no advertising, no third party.
One of those cookies has to live in your browser all the same: it is how the server knows who you are at a table and seats you in a room. It is that limited cookie or nothing — without it there is no way to tell you from the player beside you, and no play whatsoever.
So the decision is yours to revise: accept the cookie and play, or leave this page and the tables are closed to you — that is the whole of the choice.
One thing more, separate from all of this: if you sign in with an OAuth provider — GitHub or Google — the sign-in itself runs on that provider’s servers, under that provider’s policy, and it lets them track you. Accepting this site’s own cookie neither adds to that nor prevents it.