Job applicants might be expected to list relevant achievements, but there are ways to do that which convey the message "I can substantiate that I get shit done, and think I could do more in your organization" rather than "I think my blog is amazing, and now I'm going to show you how you could hit those heights".

To be fair to the author, he's writing a content piece for clicks through to a $699+ course rather than a cover letter for a job so he probably wants the hyperbolic "I've done all this in just two years. And now I'm going to teach you" tone rather than the "Over two years I've built...which is relevant because...". People that are put off by hyperbole generally aren't going to buy his course anyway.

It depends on the sector or the industry but so far all cover letters I saw were more about the applicant's qualities and personality than work achievements.