Without looking up the specs on this aircraft type, I can't give you a full technical answer, but I can give you some general ideas.
Just because a twin-engined aircraft can "fly" with one engine does not mean it can undertake the full range of its flight envelope. Sure, at cruise speed and altitude with an appropriate flight cruise power setting, twin engined aircraft can generally maintain that altitude and speed for some time, or at least maintain a very slow descent.
However, where the game changes is at low altitude and airspeed. A twin-engined aircraft generally cannot climb effectively on only one engine - any attempt to apply the kind of power needed for those types of manoeuvres will almost certainly result in severe asymmetric thrust (all the thrust coming from one side) that could lead to a loss of control. There are procedures that a pilot must learn when there is an engine failure either during take off roll, or immediately after V1 (decision speed, the point at which the pilot must commit to taking off). On take off roll, the pilot aborts the take-off on the runaway, but after V1, the pilot must take-off and reduce the engine power from the good engine, gain as much altitude as possible (turn airspeed into altitude) without stalling or losing control, and getting the aircraft back on the ground as quickly as possible. Many factors such as aircraft weight, wind conditions and barometric pressure go into how difficult this will be to achieve.
On approach to landing, it can be even more difficult, because the aircraft is sinking and flying slowly - depending on the aircraft type - perhaps only 15 to 20 kias (knots indicated airspeed) above stalling. The pilot is caught between a rock and a hard place - any attempt to climb without applying power is going to drop his speed dangerously close to stalling; any attempt to apply power is going to cause asymmetric thrust, and he risks suffering loss of control. Even applying a low to moderate power setting will cause sufficient asymmetric thrust to limit his turning ability - he will only be able to turn in the direction away from the good engine.
Looking at the video of this guy's landing, I can tell that this pilot knew exactly what he was doing. He approached along the grass median to the left of the traffic lane, keeping very lower power setting knowing that his aircraft would always want to turn left away from the road. He kept himself out of the way of the cars so he wouldn't crash into them if he got it wrong, and slid his aircraft sideways into the gap the drivers made for him. For mine, that was one outstanding piece of airmanship.
Thank you very clear explanation for a non-pilot. Pretty much like losing a mast on a ketch you end up with an unbalanced rig that tends to turn you into or away from the wind so you have to reduce sail, keep your rudder over but try and maintain enough seaway to maintain helm control.