If the dots occur BETWEEN paragraphs, this is a technique unique to this author to indicate the passage of time. Since the technique is unique to the author, and not a part of standard English, it has no name (unless the author has chosen to give it one — you’ll have to contact him or her yourself).

Ellipsis (plural ellipses; from Greek ἔλλειψις ‘omission’) in printing and writing refers to the row of three full stops (… or . . . ) or asterisks (***) indicating an intentional omission. This punctuation mark is also called a suspension point, points of ellipsis, periods of ellipsis, or colloquially, dot-dot-dot. An ellipsis is sometimes used to indicate a pause in speech, an unfinished thought or, at the end of a sentence, a trailing off into silence (aposiopesis).