OK ... Re: Apple arcade: If you subscribed with a free trial, please remember to cancel 24 hours before the free trial expires if you do not want to pay charges to continue.
Seems you can download Apple Arcade games from the App Store.
Re: "I read somewhere some days ago you would be able to see a list of players to challenge, not only friends from contacts"
You may need to choose how you share your activity:
with Everyone, Friends Only or Only You in:
System Settings > Game Center > Activity Sharing
Eg: When in a multiplayer game, you should see anyone there who allows you to, in their settings.
In Mac OS Sequoia:
Play a game : In the Chess app on your Mac, do any of the following:
- Challenge your Mac or a person to a game: Choose Game > New.
- Tip: When you start a new game, move the pointer over the items in the Variant and Players pop-up menus to get information about them.
- Play a match online: Sign into Game Center, choose Game > New, click the Players pop-up menu, then choose Game Center Match.
If your MacOS version is an earlier one, you can choose it at the top of this article, for more accurate info. Chess User Guide for Mac – Apple Support (AU)
More info. if needed: Play games on your Mac – Apple Support (AU)