I don't know that this is a generational problem. While the young have more readily been early adopters of things like Snap Chat/Twitter/etc, I have seen no shortage of short and stupid online communications from Baby Boomers and Gen X'ers.
Isiola makes a great point about cell phones. I certainly say less when browsing from that device. I'm sure some people wish I would only post on political topics from my cell.

The cell phone is an interesting case of the technology mostly forcing you into shorter communications, if you are going to use it at all. I guess you could say Twitter does that too, but a person can easily get by without Twitter, but it's hard to get by without a cell phone. These technologies change how we communicate.
Oddly though, people do seem to forget that the cell phone is more than a texting device and can actually be used to make a telephone call. When you try to call someone today, they think a.) You are having an emergency, b.) You are being waaay too intimate with them, or c.) You are an old person that doesn't realize phone calling is wrong now. But I digress (as the long winded poster that I am).
Another important factor that people are not discussing is the reinforcement that one gets for shorter communications. If you make a really long post, people may not read it, and if they do read it, there is still a good chance that they won't respond, and they especially are not likely to respond with the same level of detail because it is time-consuming to do so. The lack of response to longer, thought-out posts can easily extinguish them. I often feel frustrated that I put a lot of effort into things that just seem to go unnoticed, save for an increased view count.
If you make shorter posts, however, people have a back-and-forth with you, and they "lol" at your snark and mini-witticisms. It's fun to make small talk like that (literally small). It's just easy to think that this is the communication that matters most because it gets the most response, when often it's a lot of people saying a lot of nothing.
Ultimately, I see it as a breadth VS depth problem. Many of our digital technologies overemphasize breadth, and therefore brevity. It is a chicken-and-the-egg argument as to whether these technologies make us stupid, or if our stupidity is what creates the demand for them. They aren't entirely stupid though because breadth of knowledge IS important. The trick is really learning how to transition from 'breadth' down into 'depth' when it's appropriate. Of course, the opposite can be true as well. Mark Twain once famously wrote that he would have written a shorter letter if only he had more time. We all could stand to better think about how our time is spent in reading and communicating and whether we could stand to spend more time on a subject to fully understand it or commuicate it, or if we could benefit from a more concise formulation of our points.