A game of chess, even in the 3d world, takes part on a 2d plane
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.
