Why this LED strip is emitting light if any driver output wire alone is connected to either one of its terminals but only near the floor?
There is often much capacitive coupling of the net power in a building or room.
On the floor and walls might be even an invisible very thin layer of condensed water and dust that results in a huge capacitor to the rebars resp. grounding. 

The LED strip is lighting since the phase/hot pole is also somehow coupled via the power supply into both DC wires. Or it is coupled in the body of the person that holds the strip and then into the DC-wires. 

So it does not matter which power supply's pole is connected to which LED strip's pole since the AC is anyway rectified by the LEDs.   

But this current is very tiny, i.e. the strip is only very dim. Modern LEDs are very sensitive, can light up with those tiny currents.
Since multimeters have huge inner resistance, it is possible to measure the (fluctuating) voltage as well.