Once one gets past the rather mean-spirited depiction of the 'typical' grammar snob, I'm more in agreement with Chalabi than not, though I think what she is missing is the question of audience. If I'm editing a novel and I miss catching that a character says 'less' instead of 'fewer', well, that's not as big a deal as if I miss that in a government paper which represents more formal writing; and if I miss that in an academic journal, I might actually be allowing a significant error through because precision of language is crucial in describing an experiment or scientific concclusion. The example Chalabi uses of how of the dictionary recognizes modern usage more readily than grammar snobs is the word 'literally', but her narration glosses over the fact that we can see in the video that the dictionary entry clearly identifies the updated meaning as 'informal'. So if my daughter uses 'literally' to mean metaphorically as she rants about her roommate, I'm not about to interrupt her with a correction. That would be mean spirited and silencing. But if she uses 'literally' metaphorically in a paper she's handing into her English prof, I'm going to point that out. I try not to interrupt speakers with grammar objections, and I'm okay with informal English in emails and blog posts or whatever; but if one is writing in a formal context, formal English is to be preferred, though clarity trumps all, always.
One reason to have editors is to help people express themselves in formal contexts when they have something significant to say and want to get it right: When speaking to power, it's sometimes helpful to speak Power's dialect.
But I agree with Chalabi that constantly correcting someone's grammar is silencing. The meaning of the phrase "I ain't never" is perfectly clear, even though grammatically incorrect for formal English. Recognizing that it is part of black dialect is important because, for generations, blacks underperformed in schools partly because every time black students spoke in their mother dialect, a white teacher (or assimilated black) would interrupt and tell them that they were wrong. I'm not sure the Ebonics movement is entirely the correct response here, but ignoring the issues of class and race and gender conflict inherent in language is worse. There are more English speakers in India than there are in England, so it's not entirely clear to me why only the Queen's English counts. If I am editing a novel by a Chinese Canadian, and the author's language usage shows vestiges of her Chinese heritage, I'm not sure I want to entirely edit that out. Maybe yes if it's a fantasy novel intended for a general mass (probably American) market; but if it's a novel about life in China, or about the Chinese immigrant experience in Canada, not so much! I want to retain the author's authentic voice, as if she were talking directly to the reader, though enough editing so that doesn't become a barrier to reader's comprehension. For me, clarity is always king. The reader should feel as if the author is speaking directly to her, but not with such a thick accent as to not be understandable. The trick is to find the right balance between reader effort (sometimes the reader should have to work a little to understand!) and reader comfort (but they have to keep reading!). That, in part, depends on the significance of the work (literature or escapism; is the reader trying to experience a culture or solve a whodoneit?) and in part on the intention/wishes of the author on dimensions such as critical acclaim vs sales....
So yes, interesting video expressing an important point. As an editor, I have a responsibility to help the writer fit the grammar to the intended purpose and audience, with the default as 'fix the grammar' because that's why clients seek out editors. But outside of paid editing work, if they don't ask, don't tell.