Would you say a game like Chess requires safety tools? What would those look like?
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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.
In addition to what others said, while chess doesn't have many built in safety tools, the rules of chess venues (such as tournaments) do function as those tools. For example there are rules about personal conduct, noise levels in playing area, and designated people to speak with if you have an issue (usually arbiters or tournament directors). All of these rules, while not perfect, ideally serve the function of making the playing space safer for the participants.
I think 'sportsmanship', whether implicit in a competitive game's culture or explicit in its rules, is another safety tool too, in that its supposed to draw lines and set boundaries on conduct and ensure everyone is comfortable while participating! Safety tools are not unique to tabletop games, its just down to what language we apply :)
There is a code of ethics that's been promulgated by the USCF but there is actually a LOT of problems with questionable/borderline behavior at chess tournaments. It was hotly discussed when I was running tournaments back in the 1990s, and I don't know that it's resolved.
For example, here's International Master Jeremy Silman reminiscing about "odd behavior" he has experienced at the chess table. Ultimately his only response is that if it crosses a line you should report it to the arbiter or tournament director. But we all know that without clear lines pre-drawn, leaving it to the judgment of someone often just permits the standard old discriminatory lines to be drawn. So actually I think chess is a good example of a competitive game that is really digging around trying to find some way to address the safety and comfort of participants.