Kbin and Lemmy are both different pieces of software that can be used to spin up an instance of a reddit-like news aggregator. Both speak the ActivityPub protocol, a common “language” that allows instances in the Fediverse to connect. In theory a Lemmy or KBin instance can connect to all other Fediverse instances via ActivityPub, no matter whether the server runs on the Lemmy or KBin Software or it’s an instance of Mastodon or Pleroma. But the administrators of a particular instance can restrict which servers they want to federate with, but that is not a feature of the used software. A caveat is, that in practice there had been some issues with federation between Lemmy and Kbin servers in the past, at least I heard so. You could regard this as software bugs and in current versions that should be better.
Also a reason that many people choose KBin over Lemmy is that supposedly, the original Lemmy developer has some far-left “tankie” world-views and runs the “lemmygrad” instance. Many instances defederate with that (and maybe other Lemmy instances), but those are social aspects, and not an issue with the Lemmy software itself.
Definitely the opposite of “light”, but you mentioned chess and if you’re into something similar but very different, you might try learning #Go together on online-go.com. That site has a very short introduction into the game under the Learn tab, but it only covers the very basics and initially you will have no idea what you’re doing. The rules are simple, but there is a lot of complexity that arises from that and professionals study the game for years. But even as a complete beginner it’s fun. Full on 19x19 games can take a long time, but games on a 9x9 board are fairly quick, comparable to a chess game.
Still, this would be a journey. If you want something not turn-based and relaxing to play while chatting maybe try something else but I can’t give any recommendations.