The last part of this sentence ("that what it is that you are worrying about is not actually happening") has a lot going on: a cleft construction (with dummy subject "it"), adjacent "that" and "what" subordinators (with another "that" subordinator a few words later), two verbs in progressive aspect, and negation. Your fix gets rid of the cleft construction and makes the sentence much easier to read and understand. I would certainly prefer it over the original.
If that so, why would the presenter put "it is that" in the sentence?
Cleft constructions are often used to emphasize part of the sentence. In this case, the presenter emphasizes "that you are worrying about". I don't think that such emphasis outweighs the cost of the more complex sentence structure here, but to a certain extent it's a matter of preference.