You understand the product correctly. It's all done through the camera, there's no sync box of any kind.
The most important thing is to avoid having a strong source of light in the room that might throw the camera off (e.g. if you install the camera at the bottom of the tv pointing up, keep the ceiling light off).
Yes it will work with a 55inch tv. When you first set it up you will mark the corners of the tv in the app so that the camera knows where to look.
It's a very good product at it's price point. I recommend trying it at least.

Good evening, yes, there is no history of box or other that could possibly cause loss of quality or other problems of HDCP in particular. But the fact that it goes through a camera sometimes generates problems at the level of the global lights of the rooms which can come to distort the results of colours as well as a light shift. Also I personally haven't found a way to turn it off automatically, so expect to have to turn it off every time you don't use it if you don't want the lights to stay onThe camera itself (which could possibly create fears in some people about having a camera that continuously films its screen as well as the people who approach it).