Looking at the Mode S transponder graph, I get a different impression of what happened.
First, as far as I know, the "speed" being sent from the transponder is IAS, not ground speed. What it appears then is that the aircraft accelerated to near 116 knots and took off. At this point the climb profile is immediately abnormal. The plane is climbing steeply, but the IAS is immediately decreasing, instead of pilots making sure the speed stays constant or accelerating. Whatever their throttle settings or whether they have 2 or 1 good engines.......clearly the pilots are not monitoring their speed (seen that so many times now) through the departure climb, and they never regained that lost situational awareness.
For a full minute after take-off, the pilots keep the same rate of climb, but the speed decays every so slowly and gradually. Finally, at ~105 knots the plane gently stalls (From reading ATR-72 specs this is about the normal stall speed when clean and heavy), and we see a immediate reduction in the rate of climb. But it is still climbing....slower, but still climbing and still recoverable. Wings lost a lot of lift, but the AoA and high engine thrust still pulling them up, but unable to maintain speed and going to be in deep trouble if don't immediately start proper stall recovery procedure.
Then in those crucial seconds the pilots do what so many other pilots have done before them. Instead of gently easing the stick pressure and letting the engines pull them back onto the curve, they pull the nose up further and now the speed REALLY drops off. Now they got no speed, and losing altitude. And that's where they hold the nose all the way down, staying below stall speed until they crash. Look at the crash video, nose was kept above the horizon......all the way down until hit the bridge.
I don't buy the "engine failure" reports. It does happen, but statistically it is so very rare on these aircraft, and besides this aircraft is capable of a single engine departure (albeit tricky). We know that instead from crashes that depressingly the single most probable cause is pilot error, particularly in this neck of the woods.
"Engine failure" is probably what they thought or yelled in the few seconds they had during a high workload environment as the only thing that made "sense". Throttles set high/full, my nose is above the horizon, but the plane dropping out of the sky......hmmm, must be engine failure! Particularly as we know a lot of these pilots have probably never experienced a real-world stall/near-stall situation before. We've seen this before on several crashes, same thing on Colgan Air, AF447 etc. In the confusion the pilots brain just can't detect the reason they are descending with throttle levers pushed up and nose up is because they are stalled. "Engine failure" is the only rationale explanation that comes in those confused moments.