Did I just brick a non-rooted device?
The device was not bricked. After a few hours I held down the power button again, and the frozen screen was replaced by the "no battery" screen. After charging, the device is back to normal. I caution users of this particular device not to use apps that try to force the systemwide screen orientation.

It was lucky that the battery was nearly empty when this happened. I suspect that if the battery had been more charged, the wait could have been significantly longer.