Without the YouTube video your question is unclear.
But does EME makes a requrierment to ᴡatch concerned protected videos this way
What is "this way"? Linking "this way" to a YouTube video is, to me at least, the worst and laziest thing you could have done. You should use real words to describe your problem clearly. Is EME actually important here? I doubt you would only just have gotten this problem because of EME, and without video downloader programs you would have this problem anyway.
How you phrase the question is important. You start out with a solution (that doesn't work), move into a question that is only tangentially related to your actual problem (a site making it difficult for you to download videos), and then moves on to "I don't want to pirate/redistribute videos".
You've only really hinted what your problem is in your question, and then you've asked it in an order that is nonsensical and full of unqualified assumption about what we know about your problem.
If you want help then tell us what your actual problem is as clearly and succinctly as you can. Then tell us what you tried so far, what used to work and why it no longer works.
At a quick glance I cannot tell if the video is an actual example of what you get or simply a mock up or even if the quickly passing subtitles (which are in a foreign language) are important. In short it does not help people here without having to spend time working out what the video is telling them. Many people watch films or listen to music while using their computers and opening "yet another" video or having more noise can be aggravating and turn them off of answering your question or even reading it in the first place.
Perhaps a better question would be
what is it about EME that makes it difficult to download a video for offline use?
But that is actually very broad and implementation specific and potentially still off topic for being vague and broad. It depends a lot on how the site is coded and media is transferred and chances are you would need downloader for every site as there are a lot of ways it could be implemented, particularly where DRM is concerned.
Or, more simply, one you could ask your video site of choice (but not us as it would be off topic here)
Do you have a program that would allow me to watch your videos offline?
Amazon (and other suppliers) often have Android or iOS apps which support downloading for offline use.
Encrypted Media Extensionsis just a standard. A standard isn't going to standardize, the process of preventing downloading a video, and creating a local file. Other users have expressed the reasons it was unclear. I am not going to choose to repeat those reasons.