"Il parle, merci !"
Parler can be transitive and intransitive. In the transitive case you are discussing one's ability to "speak" or a subject of which you are speaking.
"Elle parle très bien (le) français." - is a transitive sentence.
I don't think this lesson applies though. I would agree with "Il dit, merci !"
Agreed on the dual transitive/intransitive possibilities of verb " parler". However, here, with the comma after "il parle", the person saying "merci" is not the one who speaks. if you want to mean "he says thank you", you don't use a comma and you say "il dit merci" or "il dit : merci". And the verb is "dire", not "parler".