A very picky English teacher would change that sentence to:
"Do you know about whom he is speaking?"
as there are at least three things in that question that are considered less than ideal for very formal, very standard English.
The onen that you found was who/whom. "Who" should be used for subjects; "whom" should be used for objects. And so, you're right, it should be "whom." But most Americans mess that up and (incorrectly) use "who" all of the time.
So, if you keep reading that blog, you can know that you know English better than the writer does! :)