Twitter as the Source of New Slang? Maybe.
It is quite a new piece of slang, the simple sentence “That is all.” Perhaps it is due to the fact that Twitter, in English, only allows for 140 characters. In that way, tweeting in Korean is far better. The use of the sentence “That is all.” is a way of pointing out something without any extra details, largely because no other details are necessary, and that the statement itself should be entirely self-explanatory.

Simple Examples May Make the Point
Example #1: Steve Jobs cannot be replaced. That is all.
Example #2: Lady Gaga is da bomb. That is all.
We can have all sorts of debates on whether or not either statement is actually true. However, the point is that the writer believes wholeheartedly that it is true, and that there should be no dispute. No long explanations are needed, in the writer’s opinion. That is the purpose of the phrase “That is all.”

Twitter Only?
Twitter has changed the world in many ways, some great, others not so. “That is all” is very casual in writing. Usually, we don’t use the phrase in spoken language. Oddly enough, the meaning and the intent of the use is clear, but the places that it can be used is not. It definitely is not appropriate in formal or academic writing of any sort. That is all.