I think this is the only MLA style that is tied to the offerings of a single commercial entity. That seems weird to me. Does Twitter own the idea of a tweet or has it escaped into the general culture?
Strange indeed that they use the word "Tweet" when there are many other microblogging services, including Facebook. How does one cite Status.net?
[Nobody][Ever]
"[...] and the medium of publication (Tweet)."
Does that imply that you can just make up a word for whatever the medium of publication is?
General culture. It seems standard practise now in print and video journalism to quote tweets about whatever current affairs you have: "user FooBar on twitter said 'I don't like this thing'"... regardless of whether FooBar has anything to do with it at all. A lazy way to get bystander comments from people who have even less of a relationship to the happening than bystanders do.