"Shake hands before the match" and other courtesies ARE (very mild) safety tools, framing and grounding the game in good conduct.
Sure, that makes sense. Also, since games like chess are explicitly competitive, where one player is trying to mentally dominate the other, the players would presumably already know what they were getting into.
I did in fact write a story game that uses chess and has safety tools! But yeah in general people have an understanding of what chess is, and what the pieces do, and what the outcome is. People know what happens in a chess game before they start playing, even if that's approximate. There's very little uncertainty in content, and then of course chess doesn't necessarily come with narrative, although it very easily can.