I'm asking out of pure curiosity as I'm not native English speaker.

Chess leading to madness - I think I get the joke here, and well, who knows, some grand masters have gone mad (although I'd guess some will dispute if there is clear link between madness and chess).. but delinquency? I'm not native English speaker so maybe I'm missing the full meaning of this word but translator tells me this word is clever way of saying 'crime', how on earth would chess lead to crime :) (other than, if played on paid time it is, well, crime of a sort, but same as browsing through social media).

It might be a reference to:

https://gizmodo.com/chess-was-once-deemed-a-menace-to-societ...

Drugs lead to delinquency (crime) and madness. Depending on your view that is what some might say drugs do.

Since the OP said they had to block chess because of phone addiction, the joke is just replacing drug addiction with chess. Chess (drugs addiction) leads to delinquency and madness.

I think it's just a joke about how chess (generally considered somewhere between harmless to noble) was used as an example of contributing to negative behaviour by the poster they answered to.