What present did the children give the Professor in "The Egypt Game"?
The children gave the Professor the gift of the company of others. Through his secret and silent observation of their game, he was inspired to care again about living.
The Professor explains what the children did for him in the form of a story. He relates that when he was a young man teaching at the University, he fell in love with one of his students. The Professor himself was always "a very quiet and reserved person", but his vivacious Anne brought enthusiasm, optimism, and fun into his life. They were married, and traveled much together, he doing research and she working with the suffering people of the forgotten places they visited. Tragically, in one particularly downtrodden area, there was an uprising, and Anne was killed.
The Professor returned home alone, with "no desire to teach". He moved into Anne's store, but "broke off...the contacts that Anne had made and let the store become a junk shop". The Professor says that "the store and (he) became dusty junkyards, and after a while (he) didn't care".
For twenty-five years the Professor lived in self-imposed imprisonment, having eliminated contact and involvement completely from his life. It wasn't until the children started the Egypt Game in his backyard that the Professor took an interest in anything, and after he finds the courage in himself to help April, he discovers the joy of community and renewed interest in his work (Chapter 23).