First off, just because Movie A is out on DVD doesn't mean Movie B (released the same day) will necessarily be out on DVD as well. Particularly if Movie A's gross was 10 times that of movie B, or Movie A was marketed to a worldwide audience, while movie B's was marketed only to a single political niche in one country.
That being said, 13 Hours does appear ...
Doing that on purpose is a cinematograpy technique called Shaky cam:
Shaky cam is often employed to give a film sequence an ad hoc,
electronic news-gathering, or documentary film feel. It suggests
unprepared, unrehearsed filming of reality, and can provide a sense of
dynamics, immersion, instability or nervousness. The technique can
be used to ...