Jinja Shinpō introduced another video created by a group of Shinto priests in Tokyo, in the February 28th issue. This video was created by priests in rural Tokyo, and includes both a recitation of the haraëkotoba (the standard purification prayer) and video of misogi, purification in water.
Note that “rural Tokyo” is a thing, as you can see in the video. The prefecture extends up into the mountains, and there is no city within it called Tokyo, so there are no grounds for saying that this is “not really Tokyo”.
The purification prayer is standard, and recited before all matsuri, although it is very unusual for a group to recite it, particularly while reading off a text. Misogi is less common, but it is an established part of Jinja Shinto practice, and is regulated and taught by people formally appointed by Jinja Honchō. Apparently, the jinja where much of this video was filmed, Musashi Mitakë Jinja, runs courses where you can experience it, in the summer. I may look into doing that, in a hot month. (There are some jinja that do it in the middle of winter. No. Nu-uh.)
Women are allowed to participate in misogi; it just so happens that this video was made by a group of young priests from the area, and the group does not include any women. Women who are doing it do wear a different outfit, however.