I don't feel the rectangle/square example is valid, given that both alternatives follow different designs - there's no Shape base class in the inheritance example. Moreover, I don't think that switching from a base (abstract) class to an interface is enough on itself to call it composition.

The two issues the article mentions have imho less to do with the LSP itself, and more with the limitations that different programming languages have when it comes to define contracts through interfaces (not the same thing), like the lack of exception specs or non-nullability enforcement.