Unfortunately yes. There is a thin layer of glass underneath the outer plastic screen. Subject this to any kind of twisting force and it will fracture, as yours has done. The diagonal line on the screen in your picture is the crack in the glass.
It's essential to keep the Kindle (or any other eBook reader) in a rigid case when carrying it, especially in close proximity to heavy books.
No manufacturer will replace this kind of damage under warranty. That's why Amazon sell accidental damage policies as an optional extra for the Kindle.
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