It is very witty to compare this to Twitter. Just as the internet came out of military research, so too this 1920s joke was borrowing from the postcards sent home from the front in World War One. The standard format meant they did not have to be censored. The British called them field service postcards. In the US army they were given out by voluntary organizations like the YMCA, and I don’t think they had a standard format.
For more see http://blogs.utexas.edu/culturalcompass/2012/08/02/paul-fussell/