It made more sense when I followed some other links in this discussion. Read this:

  Hey.

Or this exchange:

  Statement: We got the tickets for tonight!
  Response: Yay.

It comes off as very flat or dry. Unenthused. A plain "Yay" with no punctuation would be better here. I wonder if this is the context that we're missing and others aren't providing, because I almost always use punctuation, including periods, in my messages. No one has ever complained. But with short messages, like these, I would never use a period. For full sentences, however, I can't think of any occasion outside being rushed where I wouldn't end it with a period.