I think that looking any animal in the eye shows that you have no fear of them. If you consider your own chickens' pecking order, the dominant birds look and strut toward birds lower than themselves, and those birds shy away. So, I would think that looking a rooster in the eye would be expressing some type of dominance.
Personally, I always look my roosters in the eye. I think it is important for them to know that I am head rooster and I am protecting and caring for them, they are merely helpers.
I have 2 roos and one cock. I have a rooster that imprinted on me and he has always kind of watched me, more closely as an adult. He stares for long lengths of time. I think he is trying to understand me. He is a total people pleaser. If a hen makes a fuss when I pick her up he comes over and pecks her on the head. There is one hen that he bullies. He has gotten much better, but I caught him the other day going to peck her on the comb. I ordered him "Bravo, No!" And he halted his plans and just looked at me. Then he tried again. This repeated maybe 4 times. Eventually, I said "Bravo, there is a space up there." And I pointed to the perch above him. "Go up there." And I'm not kidding you. He jumped up there! I was very suprised, but he seems to be far more aware of what I want than everyone else.
Now my other rooster never paid any attention to me and spent all his efforts feeding the women. When he reached 5-6mos and he started that watching behavior, he also started standing with an aggresive posture. After a few weeks of this he started attacking my legs and flying at my face. He went into immediate rooster training.
Both roosters (1.5years) and now the young cock stare at me, but so do some of the hens and the guineas.