You read the licence wrong. When you buy, rent, you're explicity forbid to do public playing: that means you cannot show other people the material, they have to pay for it. That way they're sure you dont mount a cinema in your home and invite the whole city.
That's simply not true. Public playing means that you cannot go to a part and project on a screen (as an example). In the confines of your home is not considered public playing.
