Add your video and make it play automatically. You can do this by clicking the Playback tab under Video tools. In the Video options group choose Automatically next to the Start option.
To advance to the next slide without clicking (bearing in mind that the video is the only animation on the slide) you have to choose the Transitions tab and set a timing in the Timings group, check the After box and add a transition time.
You might think that the transition time should be at least equal to the duration of the video, but this is not the case. The auto transition function has no priority over the video playback. In other words, PPT waits until the video is over before navigating to the next slide.
So set a timing of a few seconds to obtain the automatic transition.