Why Gain-Bandwidth Product of devices having a simple one-pole frequency response is constant?
In that diagram, there is one high frequency pole.

As the frequency doubles, the gain halves. As the frequency increases by a factor of n, the gain decreases by the same factor n. So the factor n cancels out when you multiply frequency by gain.

If the amplifier had two high frequency poles, the gain would fall by \$n^2\$ as the frequency increased by n, and the factors would not cancel.

Bonus comment - 

There's a filter response which falls at 3dB per octave, what you would get if you had a 'half a pole' response. This has constant output power * bandwidth product, as the (voltage) gain falls by \$\sqrt{n}\$ for each increase of n in the frequency, so the power output (voltage squared) drops as n. This is often used in audio testing to shape white noise into 'pink noise', so that the power in each decade is constant.