Final answer:
The Professor watches the children play the Egypt Game from the doorway.
Step-by-step explanation:
The Professor watches the children play the Egypt Game in the doorway.
Specifically, the daughter of the Professor is sitting in the doorway winding blue silk on a reel, and her little dog is lying at her feet.
This is mentioned in the text, 'The daughter of the Professor was sitting in the doorway winding blue silk on a reel, and her little dog was lying at her feet.'
Therefore, the Professor watches the children play the Egypt Game from the doorway.