That's not what the author is saying. He's saying that if you are either unable or unwilling to correctly use "your" and "you're", you are probably unable or unwilling to pay attention to the details that matter to success in his business. I agree that there's a fine line between proper attention to detail and nitpicking, but taking the author's statement in context I don't think he's on the wrong side of it.

It makes sense, but that's the danger of it in my opinion.

If you think this way, it's worth going back and examining the writings of people you admired. You might be surprised! Or not.

It depends on why I admired the people. If I admired them for their success in business, then yes, I would expect their writing to show attention to details like spelling. But if I admired them for something else, I wouldn't necessarily expect that. I'm certainly not saying that anyone who is worth admiring has to spell correctly.

Not 'the essence of intelligence' but 'one indicator of self-discipline'.