Thanks for the information. I have reported this issue internally to the team who owns the HTML5 MMR feature and they have added it to their backlog to investigate why it doesn't work when on an App Volumes writable volume. I will have them post here if they have any follow-up questions about your environment.
Just an FYI that with chrome extension version updated to 22.214.171.124, the extension seems to be working fine with App Volumes writable, as I'm no longer seeing the issue I wrote previously. However, when I attempted to playback a video from the URL added to redirection policy (i.e. Youtube), the extension icon will list it as REDR, but the video itself will not show up at all.
This happens even in the published app version of Chrome I'm using, which doesn't involve any app volumes components. Any ideas?