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First of all I haven't got the article and so I haven't read it.
Eye relief is the distance from the surface of the eye lens of the eyepiece to the front of your eyeball. The eye lens is the bit you look through as opposed to the field lens which is at the other end inside the barrel. The greater the eye relief the further back you need to place your eye to see the entire field as the eyepiece was designed for. 20mm eye relief is great for eye glass wearers. Too much eye relief and you get the situation you describe whereby you are getting vignetting of the exit pupil common with long focal length eyepieces used with Barlows which extend the eye relief. A solution would be to use a Powermate which places the exiting light cone to a point the eyepiece designer intended.
Exit pupil is the diameter of the cone of light leaving the eyepiece. If small then this cone of light enters the centre of your eye and does not extend too much toward the edge of your eye. If the exit pupil is large you use more of your eye to see the cone of light and the outer portions of your eye will exhibit some aberrations that will affect the image.
If you have astigmatism and you observe without glasses you may notice that with low power you just cannot get a good image yet with higher power the image appears much better and this is because at higher power (smaller exit pupil) you get a much smaller light cone entering your eye.
exit pupil = eyepiece focal length divided by telescope focal ratio.
Now another adverse affect of growing old is that your eye wont dilute as much as when young and therefore you may not allow the entire light cone to pass into your eye at low powers. This however is unrelated to the advice given to observe with smaller exit pupils for sharper images.
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