Fascinated by this article. I've noticed I do leave out periods (or full-stops, as we call them here) when I chat online, but that's because I send fragments of thoughts line by line - as the author said, using line breaks to punctuate. But once I've completed my thought or whatever I wanted to put across, I end that last sentence with a full-stop.
In writing online, like in comment boxes and emails, I leave out the full-stop when I end the sentence with an emoticon. I consider the emoticon a punctuation mark in itself - it's the equivalent of me saying something to you face-to-face, then ending with a grin, grimace or pout.
I've caught myself doing what the author noted - using an ellipsis (...) to sound less definite and more tentative/diffident. In my mind, when I 'hear' what I'm typing, I envision my voice trailing off at the end of a thought or sentence, showing that I'm not closed against opposing ideas or further input, that I'm pretty laidback about this whole thing.
I know, I know... being so interested in the evolving use of punctuation in online contexts exposes me as a huge nerd. But I don't care :p