I found this in the July 30, 1893 issue of the Brooklyn Eagle. Assumptions are dangerous, but I think it's a strong possibility that the article refers to our Michael Mulcahy, Papa's father. We know he owned a bar or two, and so I think it likely that he'd be attending a picnic given by the Brewers' Association. It appears, too, that Michael Mulcahy was something of an athlete - he came in second in both the 100-yard dash and the running high jump. He was beaten, both times, by Michael O'Halloran, who also won just about everything else. At least Michael Mulcahy was keeping up! The only other person who came in first in anything was Edward O'Halloran; I bet he and his brother trained together. "Mike" Mulcahy was on the games committee, as well.
While I clearly didn't inherit Michael Mulcahy's track-and-field genes, I think I've got a couple sisters who did!