A lot of user interface design is managing user expectation (things people have gotten used to, like where a "create" button is or what a "share" icon looks like) versus optimizing for long-term usability of an app (something like Snapchat, with its seemingly-esoteric UI that is actually efficient once one is used to using it).
The only reason the author gives for taking this position is that "Participating on someone else’s operating system means you’re on their turf. The author even admits that "I’m not saying either design is superior." So app companies should forego optimizing for user experience to pay respect to the platform that they're on? This is a totally backwards position; apps should respect their users. If that means following all the OS guidelines for a sparingly used app, that's fine. But if that means creating a unique UI and app flow for long-term user happiness, then the app company owes no respect to the "local conventions" of the OS.
edit: clarity