Yes it does...if you watch the video is shows that and then you hear the narrator explain the closing. Just because you use the x to close it doesn't mean it's not still running in the background, it is as the video clearly states.
If you like to try, open and app, use it or not, close it with the red X option and then open task manager and check to see if it's running...you'll find that it is.
This is only real gripe I have with 8/8.1/8.1.1 and how it closes the apps. I still drag mine to the bottom and wait for it to flip.