7:00am 23rd May 2017
Unfortunately, there isn't really a way around this. Mobile Safari will not download any part of the video file until it gets a user interaction (i.e. some kind of touch event), not even the header, which is required to know the dimensions.
In your specific example, you need to enable controls on the video so the user can start it playing. (Or you can write your own code that starts it, but it has to be triggered by a touch or click event.) Once it starts playing, the loadedmetadata even will fire, and you can do what you want.
I recommend reading this other answer where someone else was trying to do pretty much the same thing. It discusses the problem in more detail along with a working link. Also, it addresses another problem with scaling the video that you will probably run into.