Yes, by allowing you to download the video file to the browser. This snippet of legal terms didn’t really reinforce any of your points.

But it actually is helpful for mine. In legalese, downloading and storing a file actually falls under reproduction, as this essentially creates an unauthorized copy of the data if not expressly allowed. It’s legally separate from downloading, which is just the act of moving data from one computer to another. Downloading also kind of pedantically necessitates reproduction to the temporary memory of the computer (eg RAM), but this temporary reproduction is most cases allowed (except when it comes to copyrighted material from an illegal source, for example).

In legalese here, the “downloading” specifically refers to retrieving server data in an unauthorized manner (eg a bot farm downloading videos, or trying to watch a video that’s not supposed to be out yet). Storing this data to file falls under the legal definition of reproduction instead.