I think the fellow to the left of Greenleaf (far right) is the referee or other official--he does not have a cue. The next fellow, short and bald, is the one who I think is Onofrio Lauri.
10-man round robin fits with there being a referee or tournament director.
The picture is from the World Championship, 1933, Chicago.
As noted in Charlie Ursitti's website;
This was Willie Mosconi's first World Tournament appearance. In his very first game in World Championship play he faced Erwin Rudolph and was defeated 124-125. Needing only one point, Mosconi jaws the )ne Ball in the corner pocket. Rudolph got up and run 42 out. The one ball not only cost Mosconi the game , but also the World Title. Mosconi tied with four other players with a record of 6 wins and 3 loses. Erwins record stood at 7 wins and 2 loses. Mosconi could have become one of only two men to win the World title in his first attempt.
From the left:
Andrew Ponzi
Jimmy Caras
George Kelly
Willie Mosconi
Frank Taberski
Pasquale Natalie
Erwin Rudolph
Charles Seaback
Bennie Allen
Joseph Ferguson, referee
Ralph Greenleaf