Wrong. It's a simile. You can't put the word like there; its grammatically invalid.
First,
A simile is literary device that uses the words "like" or "as" to compare two ideas. [...] a simile allows the two ideas to remain distinct in spite of their similarities
Second, He's comparing two forms of the same thing, which means it's not even a simile, it's a comparison, in which case "like" is still grammatically correct.
Your conclusions is erroneous; the definition you quoted agrees with my use of the word. The sentence compares the ideas of 'writing' and 'thinking,' which are similar yet distinct.
Even if you argue with that, we've already established that grammar is not pedantic, so your point is irrelevant in that regard.
Finally, the grammatical error isn't even conditional on it being a simile. The word 'like' can only be followed by a noun, where as the word 'as' can only be followed by an adverbial phrase. It may have been confusing that I even mentioned it's a simile, but the rule (see link below) usually comes with the word, since they're so closely linked.
http://trc.ucdavis.edu/bajaffee/SAS90B/Course%20Content/Grammar%20Syllabus/Like%20vs%20As.htmQED
