Gragz, here are some wrong stuff about your run.
- didnt start looking down (you'r 1.1 tho, so that's ok)
- a little slow to open the cell
- got the keycard guy in a bad position, and spent too much time on him. You gotta fire a few bullets, and hope he throws the keycard towards your direction. I'd say you can save 1~1.5s there.
- released your strafe for two moments (before and during the stairs)
- killed some unnecessary guys before the key
I suck at this game, but those were very easy to notice. Watch your vid, and then watch Bryan's 24. You'll clearly see the differences.
Hope it helps.