It's one of those songs with a hundred meanings, I guess.
The storyteller is playing chess, maybe at a hotel by the sea (cooks in the kitchen), while others are not involved in the game (the boys play cards), or they are not really interested in it, because they (usually) play cards, not chess.
Then he becomes aware that it would take just a small thing, an accident or whatever for his whole perfect litttle world to collapse, and he could do nothing at all about it.
So, literally, the mouse that trips the wire would upset the chessboard and stop the game.
Metaphorically, it's the storyteller's life, and our own lives that could be upset by some small incident. And of course you can take this idea further and expand it to the world as a whole.
The only thing that doesn't fit is the last line! "But the truth will finish first." That means "the truth will win" (finish first as in horse racing), right? Which means "Lies and Fake News" will lose. And somebody "rich and smart", in his "noble house", "his golden chair", "won't be going anywhere", because he'll "be trapped" and roasted alive amongst his "works of art".
Now, let's all guess who that may be.