Cookies
Lobby Meadow sets no cookies today
No analytics, advertising or social-media script is loaded on any page, so nothing sets a cookie. The bar at the bottom of the screen asks anyway, so that the answer already exists if a visitor counter is added later.
What Accept and Reject do
Either button saves one entry in the browser's local storage: the name is lmCookieChoice and the value is “accepted” or “rejected”. Local storage is not a cookie and is not sent to the server with page requests.
With “rejected” saved, the site behaves exactly as it does now. With “accepted” saved, it also behaves as it does now, because the address of the analytics script in the site's code is an empty string. If a privacy-respecting page counter is added one day, it will load only in browsers that hold “accepted”, and this page will name it before that happens.
The answer saved in this browser
The saved answer shows here when JavaScript is on.
Clearing site data in the browser's own settings removes the entry as well.
Cookies on the game sites are a separate matter
CrazyGames and Poki show adverts and have cookie notices of their own, and Poki's FAQ says a guest's game progress is kept in browser cookies. Both sets of cookies come from the host after you follow a link, and the host's notice applies there. Lobby Meadow has no say over them.