To add to your point about this being an invitational game, Muddy Ruel gets mentioned in the post-game article:
"Ruel was the outstanding batsman. He often drove the ball among the spectators in the stands."
He was with the Senators at the time, and didn't join the White Sox until 1935.
A possible explanation for Ruel, McInnis, and Stengel to be at the game is that they might have been some of the favorite players of White Sox owner Charles Comiskey, and involved in his "Woodland Bards" social group. The Bards are mentioned in this Chicago Tribune article about the exhibition tours that Comiskey organized in 1913 and 1924:
http://articles.chicagotribune.com/1...al-squads-game