I'm wondering if this was the same ankle that he later fractured in the Water Torture Cell in October? That is generally considered the first link in the chain of events that led to Houdini's death on Halloween. But maybe the ankle was in a weakened condition, so the chain actually started here with his accident outside the National.
The theater still stands today at 208 W. 41st St. as the Nederlander. Watch out for pipes!