Well, this was a very short and simple test to prove the issue:
I have a Lumia 635 that is running stock OS... not dev preview (both my 1020 and 1520.3 running dev preview behaved identically, however, for sake of notation). This 635 does NOT have the Gestures Beta and it is running the old Extras+Info not the update from yesterday as evidenced by these screenshots (note Extra+Info is not at bottom of list from update too):
Booted phone.
Installed TheChive app.
Launched app... and began using for a few minutes, including navigation... not just the homepage. In this case I looked at the Best Photos of the Week gallery. The bug seemed to be triggered when I got to an animated GIF image (it's the Chive, so use your imagination).
Phone began to exhibit the symptoms of not powering on. (Seen in video)
Rebooted... issue gone, so uninstalled, and rebooted again. (Seen in video)
VIDEO:
https://onedrive.live.com/?cid=1D1CDFF85E429085&id=1D1CDFF85E429085!307809&v=3
I could not test 5 Minute Workouts, as it appears the app has been pulled. Since the video demonstrates the issue without Gestures or Extras, the question now remains-- what's the root cause of this behavior if apps aren't supposed to have this kind of effect and yet two apps are causing this?
Again, my hunch tells me it's some sort of power management thing-- ie. the "keep awake" function of a media player-- but not being a dev it's hard to know for sure unless they tell us.
PS-- You'll have to click the link to see the video since the forums don't embed OneDrive videos and I refuse to use YouTube.