Elipsis shows a pregnant pause, it can show long hesitation, skeptism, disbelief, a flatlined joke. If used with an third party in a conversation, "..." in combination with a character sprite emphasizes the fact that they are silently observing. Often this means they saw an important but unpleasant detail. "...!" shows surprise, positive or negative.
I really liked the use of non-dialogue in the work Mahou Shoujo. The text is almost completely dialogue, and so elipsis do a lot of heavy lifting. Also particular to that work is that the conversation beats are very pronounced.
Anyways, elipsis are concise, expressive, and can open new avenues to express dialogue beats. They do work a lot better with a character sprite though.