Whilst make outrageous claims to assert power is definitely a thing, I think the null hypothesis is less that they're playing 4D chess and more that people who constantly get away with stuff and constantly get told they're geniuses like spoiled children end up behaving like spoiled children. It's like for every "van Halen wants the brown M&Ms removed to audit the venue staff's attention to detail" anecdote there are 100 stars making extravagant demands who are just divas.

Zuck cheating at board games me of Elon buying a claim to being a great Path of Exile and Diablo player. Nobody believes he is, and nobody is loyalty tested into praising his ability at computer games, not even people who work at his companies. He gets mocked for it on his own website. The few people that would actually be impressed by a claim of being good at Path of Exile and Diablo know exactly how bad he is at it and find it pitiful; ironically it actually dents his reputation with a demographic disproportionately likely to be impressed by other things about him. Other people aren't inclined to think highly of him for playing those games in the first place, never mind paying others to boost his account. The reality is simply that when he's interested in a game he can't abide the idea of not being really good at it, and cheating and getting others to do stuff for you is the easiest way to appear really good at it. Especially when you're used to ignoring people calling you out...

> playing 4D chess

Also, narcissists don't need 4D chess levels of awareness and discipline to behave that way. It just emerges naturally from their base motivations.