I haven't seen either phrase before. The first one looks odd to me. The second version seems to be a reference to the benefits that come from telling a story in an interesting way. If you mumble or speak in a monotone, people probably won't be interested in hearing your story.
"There are a few reasons that presentation storytelling makes such a major impact."
In this sentence (and other sentences in this article) the bold means "telling stories during a presentation".
The article talks about reasons that storytelling (telling stories) improves a presentation.