Yes, and my guess is that they are planning on removing the standalone messenger from the web version. You'll probably need to have the FB Messenger app installed on a smartphone device in order to use E2EE. That would make it impossible to write messages on the web version (i.e. facebook.com) without having an app installed. I currently do not have the app installed and am able to write messages on the pure web version of FB on desktop. My guess is that they are enabling E2EE to get the last remaining desktop-only-and-website-only messenger users to install the app. Hope that cleared it up.
Again, my point is not that FB Messenger will stop working in the web browser altogether. My point is that FB Messenger will stop working in the web browser if you don't have the FB Messenger app installed on your smart phone as the primary device.
In a way that works well on low power mobile devices?
Most people I know using FB messenger do so on desktop via facebook.com and the app on mobile. I don't see them removing the former any time soon but if the web only version still exists for mobile users perhaps that will go.