I'm a flight test engineer that works on large (passenger-class) aircraft. We do tests related to this issue.
It actually has a lot to do with takeoff safety, ironically enough. If you lose an engine at high power, the airplane will try to yaw (turn left or right) because the engine(s) on the other side are still producing thrust. At lower speeds, with less aerodynamic forces, the rudder is not capable of keeping the airplane in a straight line. So there's a speed called "Vmcg" - "velocity minimum control ground" - below which you MUST pull back the power on the good engines to avoid going off the side of the runway (you're going to have to stop the takeoff). There's also a speed called Vmca, the airborne minimum control speed (you will start to yaw out of control).
So with less power on all the engines, there is less asymmetry possible in the event of a failure. With reduced takeoff thrust, you don't need as much rudder at any given airspeed, so your Vmcg and Vmca are both lower.
This is important for takeoff because if you have a lot of runway available, you can use it by taking longer to accelerate (by having lower thrust). As a consequence, your risk in the event of an engine failure is reduced - you won't head off into the grass if it happens on the ground, and you'll be assured of sufficient control authority if it happens in the air.
So when an airplane manufacturer builds the "takeoff performance charts", these Vmc speeds heavily factor into the takeoff planning.
Now, in this tail strike mishap, the lower weight caused the iPad to compute TOO LOW a speed. Lifting off too slow takes more nose-up (pitch) angle; lift goes up as a linear function of pitch angle; lift has to equal weight to go flying. Because of the reduced takeoff thrust, they were already planning to use most of the runway to accelerate - which put them into a corner; they were too slow to take off at the normal pitch angle, but were out of room to stop. So they pulled up until the airplane started flying - which means they pulled up high enough that the tail hit the ground (just barely in this case).