I don´t think that the formula given by you is right since β for the integrator is frequency dependent.
I have another approach:
There is, indeed, a frequency (rather low) for which the loop gain of the integrator circuit is "1" (0 dB) - and this frequnency is called by the author of the paper "unity gain frequency of the integrator loop gain". I call this frequency wi.
In a BODE diagram this frequency wi can be found at the crossing of the finite maximum opamp gain Amax and the ideal integrating curve which intersects the 0 dB line at ωo=1/Ti (Ti=integrate time constant).
A simple geometric relation shows that the following ratios are equal:
opamp_GBW/wo=opamp_wg/wi (opamp_wg=corner frequency of single pole opamp).
This can be modified to wi=1/(Amax*Ti)
I think - in the context of the article - this result makes sense, since wi (called by the author GBW of the integrator open loop gain) is a very low frequency leading to a rather large time constant in the formulas of the paper.