There is the possiblity that the ring you see is not stopping down the
objective lens as much as you think or even at all.

The objective is surely at least a doublet. As light rays pass through
the two lenses of the doublet, the rays are bent, converging. The cone
of light does not exit the back end of the doublet at the same diameter
the rays enter the front end. They do converge and more so than a
simple cone at the focal length of the binocular would show they
converge. Conceivably, for example, rays could be entering a 63mm
diameter doublet and exiting the back end of the doublet at only 55mm
before the light cone procedes to travel any further into the
binocular.

If the ring you see is wider than the diameter of the converged rays
exiting the back end of the doublet, then there is no light cutoff. If
you could focus the binoculars on infinity and then get a precise
measurment of the exit pupil (assuming magnification is as stated,
which is a broad assumption) you could perform a check on the effective
aperture. Don't close focus to test exit pupil as magnification is
always higher at close focus and exit pupil will always appear smaller.
So, in fact, the ring might not cut off any light at all.

edz