The article you linked to isn't very rigorous. The concept of "Bardolotry" was popularized by George Bernard Shaw, a famous critic and author. He deeply loved and deeply criticized Shakespeare at great length, and his writings on the Bard have been collected into various texts.
But while Shaw gave the idea a clever name, it is far older. I beleive it's Hemmings and Condel who claim that if readers don't like Shakespeare it's because they haven't understood it (there are a number of brief poems and introductions to the Folio). Ben Jonson's poem in the First Folio in a certain sense elevates Shakespeare beyond humanity with the great claim of the poet - that he was "not of an age but for all time". In Jonson's book of musings Timber, he specifically says he loved Shakespeare as much as possible on this side if "idolatry". So the 1620s are the latest point where we can say treating Shakespeare like some sort of God was criticized in print. Yet Jonson does go on to say that "there was ever more in him to be loved than censured".
As to the criticisms you cite aren't very sophisticated. The point about "seeing Shakespeare everywhere" is that people in the real world use Shakespeare to express themselves all the time. I just watched an interview last night with a doctor from rural Russia and he referenced "Romeos and Juliets" while making a point. The discussiin had nothing to do with Shakespeare or art or drama, it's just that Shakespeare's work is a deep well that people all over the world draw from to express their points. See for example Marjorie Garber's discussion of Lady Macbeths in politics and how Hilary Clinton was called Lady Macbeth in American news and cartoons, despite there being no specific connection between Hilary and Lady Mac. "Lady Macbeth" has come to mean "a powerful woman men should fear" to many people, and such meanings get passed around in all sorts of culture all the time.
Your critic misunderstands Bardolotry. There are very reasonable criticisms of it though. I recommend the London Review of Books article "Bardbiz" and it's subsequent famous literary flame war discussion that dragged on for years in the 90s.