Who was in mortal danger? The video showed no evidence of a gun being aimed at anyone, simply up the stairs. It's also not assault unless there's motive. Without a physical or verbal act indicating unlawful use or potential use of violence, it would be hard to prove assault. (You might be surprised when you look up case law on this)

Your civilian scenario isn't exactly congruent because you are missing the legal authority point. If you are a civilian with the authority to search a building (your house when you hear a noise at night for example), then you you would be justified in clearing the building in the same way the police did. The response of deadly force depends on if there are alternatives to that use of force (and greatly varies by state). In this case, the alternative to the occupant using deadly force is to comply with the warrant, and if necessary, sue in court for any damages.