Update 3: Thankfully, there are several commenters who are much smarter than I and have pointed out that the term "nonimmigrant" does not mean what I think it means. To me as a layperson, nonimmigrant sounds as if it means people who are not immigrants -- ie, American citizens who were either born here or who have American parents. However, in immigration law, the term nonimmigrant means people who are here temporarily for a specific purpose (tourists, students, etc) and who have to leave the country once they're done. Even though they're incorrect, I'm going to let my previous updates stand because so many people have already commented.
Secondly, this whole episode demonstrates quite a bit about how this administration handles itself. First, they didn't bother to go through the normal channels to make sure it was properly vetted. Whole departments were left completely out of the loop until it had been released. Once DHS was made aware of it, they tried to change it so that valid visa holders wouldn't be affected. This was overruled by Bannon.
In addition, someone in DHS and someone in the State Department knew about this document on Friday. Technically, when they say it's not a travel ban, they're correct -- it's not. It's much BROADER than a travel ban, in that it doesn't just preclude people from visiting here -- it strips valid visa holders of their ability to be here. At all. And they knew that on Friday, but did NOT release it until yesterday.
This should now be considered to be part of their MO. It's not just what they say in public that's bad. It's also what they're already enforcing WITHOUT telling anyone that we should be concerned with.