My question is the following:

This morning I was at a meeting for work, and the gentleman sitting next to me had a couple of cuts on his face that looked fairly fresh (one apparently from shaving and the other from a pimple). Papers were passed around the table, which he touched before I did. Immediately after receving one of the papers, I wasn't thinking about what I was doing, and I rubbed my eye. Later in the meeting I saw him rubbing his face in the places where he had these cuts, and I became concerned that I could have put myself at risk if he has HIV. I know that some health care workers have been infected by getting infected blood in their eyes. If he rubbed his hand on one of these cuts before he touched the papers that I then touched and rubbed my eye, what kind of risk would this represent?

Health care workers who have become infected by blood exposure to the eye have been splashed with significant amounts of blood that went directly from the person's vein into their eyes. What you did is not a risk for HIV.