Although nothing was actually shown in the video - it dismissed several seconds after 'Send' was tapped. With this design, where the whole message thread is shown, I think it would be better to have a 'Done' button up at the top, in case you want to reread messages or send a second reply.
I think that defeats the simplicity of this design. If you plan to view the thread / spend some time deliberating a response you just tap the notification to be taken to the Messages app. The reply action gives you a chance to respond and kill the notification in a single action — useful.