Clear skies, no LiveATC but reports of single Mayday call, gear out but no flaps and no control inputs visible in the grainy video. Something has to go really catastrophically wrong with a modern jetliner for that to happen, like the very dense flock of birds in Korea with the 737 a couple of months back.
The very short intersection takeoff seems like a good hint (and terrible practice), but all gears and engines look kinda OK from the outside. If they‘d scraped something on takeoff hard enough to take out both engines, there’d probably be some visible damage, or at least some gears sheared off.
EDIT:
Fully agree with the speculation in light of tragedy comments, but aviation is a bit of a special case. The reason it’s so safe is because an awful lot of people immediately start looking into potential reasons and then spend years getting to the bottom of it. The initial speculation is like an exercise: what could have happened? What if I’m in that situation, and need to act now, without knowing much of anything? If you do that a couple of dozen or hundred times throughout your life, it really builds a foundation for when an actual emergency ever happens to you.
It’s a bit like the reason most flight attendants in the emergency exit jump seat across from you won’t talk with you during the actual takeoff and landing: they‘re mentally walking through a potential emergency and what they‘d then need to do. Every single time. So if it ever happens, there‘s muscle memory, 10000x over.
EDIT 2: see the Flightradar24 comment below, it looks like they did backtrack and use the full runway.