Of course there are times when it's pointless and prattish to quibble about people's grammar.
But I do think that it's important to correctly distinguish, for example, between "infer" and "imply", "refute" and "deny", "mitigate" and "militate", "prescribe" and "proscribe" and so on.
If you don't then the pairs of words may become used interchangeably to the extent that they become regarded widely as synonymous and the language becomes impoverished and more fuzzy.
It's interesting too that Fry himself makes his case using perfectly good standard English and recognises when he purposely deviates from it to make a point (e.g. "none are" rather than "none is"). He was clearly taught properly. Would he prefer that present and future generations are not taught these rules and distinctions?
I'm unimpressed, I'm sorry to say. Though the animation is great. Fond as I am of Stephen Fry, this is a cheap trick- he says that the thing that annoys him most about grammar pedants is their assumption that he is within their ranks, and then goes on to criticise pedants on the basis of all sorts of assumptions about them, without any evidence that any of it is true, or that he's ever met one.
The fact is that people's interest in language (if they have any) is going to express itself one way or another, and one way, looked at from an unsympathetic point of view, is irritating linguistic pedantry for the sake of it. But only from that point of view. You might think it's pedantic to distinguish between adding 20% to add VAT and subtracting 16.66% to take it away (many people do) but try running a business without that level of pedantry and you'll soon regret it. And while we're in the business of teaching children to read and write, it's just as well that there are people prepared to debate this stuff, so we do at least know what we are supposed to be teaching them. I'm not saying that language will not evolve, just that there's every reason to try to analyse the evolution and let it evolve for the better, not degenerate into a collection of unthinking cliches and meaningless verbal derivatives.
I know it's kind of pathetic to come up with a rather pedantic response to this, but I do think Fry is, if he's making a point at all, is making one that doesn't need making- that there's more to life than pedantry. We know that; like there's more to life than bird-watching or fishing or stuffing mushrooms. I suspect he only did it because he doesn't want to be seen as a stuffy pedant.