Mea Culpa, Cliff, I thought you were asking why I used the tag, as if that mattered! Indeed the old mess games were still around in my day, and I believe still are. Hicockalorum, mess steeplechase, I believe there is an unhealthy interest in Artillery as well!
Interestingly this definition has the phrase originate circa 1936;
"To drink a container of beer without pause, My Lord"
"No doubt popular with the younger generation!"
"Quite so, My Lord".
chugalug - Definition from the Merriam-Webster Online Dictionary
Your game I remember as 'Do You Know the Muffin Man', but like Brakedwell I've probably misremembered!