I don't see a single-engine failure causing that kind of extreme attitude. These planes are designed to (and have survived) single engine failures at VR, V2 and immediately after rotation and positive rate. While a significant amount of rudder would have been necessary, unless the engines were on the wingtips, I don't see the asymmetrical thrust causing such a violent roll and pitch down.
From the video, they were anywhere from 70-85* nose down. Even a stall wouldn't cause such extreme flight angles, unless they stalled REALLY hard in a very nose-high attitude near the ground. I guess that's a possibility. If there was a single-engine situation and they overcorrected for a nose-high "let's get the hell out of here" attitude and rendered the thrust they had mute, then hard-over'ed in an attempt to break the stall at the peak of the "climb trajectory", then they could have entered that flight angle. But that's difficult. A "perfect storm" of sorts.
Older 37's suffered from rudder reversal/hardover due to hydraulic fluid being ludicrously cold. I guess that could also be a possibility at low speeds and altitudes. I can't remember if Boeing corrected the rudder actuator, or simply advised for training to recognize and correct the problem if it ever presented itself.
I doubt suicide played into it. As others have stated, it's just too easy to accomplish either during takeoff or during cruise/descent.
I've heard this was on their 2nd landing attempt. What I'd be curious to know is it this happened on a 2nd pass, or immediately after initiating a go-around. If immediately after, then any of the scenarios, including spatial disorientation, could play into it.
If it was on a 2nd pass, then who knows? Rudder reversal/hardover? Engine failure during a 2nd abort combined with overly aggressive control input leading to a stall (perfect storm type incident).
In the end, it's best to wait and see what the investigation brings. It's easy to sit and point fingers after only have a few seconds of dark, grainy video footage as the only piece of evidence. The boots on the ground will have a much better idea, and probably already do.
I'll be keeping those killed and effected in my thoughts. Hopefully some good can come out of this tragedy to make future flights safer.