Anyone who understands what "proof of concept" means is going to see that your presentation is not proving the important part. It would be like building a rear view mirror to prove that an automobile is possible.
So let's say that there is header info and you scan it on your local search clip and you scan it on the remote target clip and you compare the two and they match. What are you going to say, "See? It can be done. So all we have to do now is index all the video on the Internet..."
If the remote site is friendly... that is, they are willing to cooperate with you... then you might be able to pay them enough money to scan the videos at their end and keep track of what they have and then it's a simple matter of saying, "Hey YouTube, do you have any clips from Shrek?" And they respond yes, and you're done. However, if your goal is to monitor the Internet to find out if anyone is using your video clip anywhere, then you're either going to have to (A) download billions of hours of video so that you can index it all, or (😎 get millions of web sites to cooperate with you via the Shrek example.
As for header information, every format is going to be different and not every clip is going to have reliable, correct information. For example, if I rip a Shrek DVD and post it somewhere, I'm not necessarily going to take great care to make sure that the video headers correctly identify the clip as Shrek so you'll have a low chance of spotting your clip.
You're really focused on whether or not this can be done in PHP. The answer is that PHP can work as a sort of shell language to control whatever video player codec reading binary header gathering gizmos might be necessary to get some info out of the clip.
Please investigate ffmpeg. It can read TONS of data about video clips. More data than you need. And yes, ffmeg can be controlled by PHP but also by any other language (Python, ASP, Java, etc etc etc.) The shell language that controls ffmpeg (or whatever tool you use to extract data from video files) is only a secondary concern.