It’s because 3d chess is a sci-fi trope. There are a few versions, but it probably became most famous from the Star Trek version. 3d chess is ostensibly more complex, although the precise rules are usually not described in fiction, and the people who are very good at 3d chess are demonstrated to be extremely smart and tactical. Having a sci-fi character win at 3d chess is itself a trope to demonstrate that the character is a genius. In those examples, often the opponent will be overconfident and derisive of the character’s strategy, only to be humbled by the loss moments later. It’s a way to showing the character is cool headed, gracious in victory, and leagues ahead of his opponents.

The 4d chess meme was an escalation of a sarcastic exaggerations of the trope, like a way of saying a moron is just doing something obviously stupid is really enacting a super-strategy that you just don’t understand.

3d chess is a thing. It’s annoying to play.

I prefer 5d chess, myself

it seems like they usually use it as a farcical example of “someone who thinks they’re smart”.

I’m over here doing 5d chess like Trump with the economy, immigration and water pressure. Basically playing myself because no one wants to follow along.

Is chess not 3D?

Edit: Still playing 1D chess 😭

Yeah, but this one goes to 11.

You have unlocked the stylistic tool of the hyperbole.

3D Chess is easy, first player always wins just move your white bishop across the 3D board until the king is mated, 4D Chess is probably the same way, who can say but it is at least harder to conceptualize.

people can imagine 3d chess, whereas 4d scenarios are much harder to imagine

Not everyone - I’ve never even heard of 4d chess.