The eNotes Study Guides don't provide a chapter-by-chapter summary of The Egypt Game, but I can provide a brief overview summary for you. April and Melanie and four-year-old Marshall discover a loose board in the fence surrounding the disused storage yard behind the "Professor's" antique and curios store--actually, no one knows anything about the so called "Professor," including why he is so called.
It just so happens that chance has sent the Professor upstairs to a seldom entered storage room in search of something for a waiting customer at the precise moment that the girls drag Marshall, unfazed, clutching a security stuffed toy called Security, through the opening in the fence. Their commotion draws the Professor to a time-soiled window where he witnesses the reaction of the girls to his storage yard. When he returns later out of curiosity to see what they were up to in his yard, he discovers they have built a "temple" to the bust of Nefertiti in an otherwise empty shed. Thus begins the Egypt Game adventures.
The story takes two separate paths from here. The first tells of the girls' adventures in Eygpt land and sojourns at the library to discover facts and lore about Egypt. The second tells about the girls' friendship at school and how Melanie helps April, originally from dramatic, flambouyant Hollywood, to shed the drama and flambouyance and fit in sensibly at her new school--since April is newly arrived from Hollywood. As the girls expand their understanding of Egypt--which the Professor silently witnesses in pleased wonder from his upstairs window--dangers engulf the children at their school and on their neighborhood street, Orchard Avenue, after a schoolgirl is found in a nearby marsh, murdered.
For the children's safety, they are kept indoors to play, which of course means that the Egypt Game is neglected during this time of danger--until Halloween--when some fathers take a big group of children out trick-or-treating and the Egypt Game is discovered by some of the big boys at school, who are promptly added to those who have been initiated into the game to continue to ensure its secret status, secret to all but the Professor who has watched every development with benevolent interest.
The danger continues when one night, as an extension of the Egypt Game, April and Marshall return to Egypt Land to retrieve April's math book and a man attacks her. Her fate is sure to be that of the girl found in the marsh except that the Professor has been on the watch and, seeing the attack, calls out and calls for help, thus rescuing April from peril and doom. In the end, the Professor's fence is mended and the girls are honored with a key to the padlock on the door of the storage yard so they can continue the Egypt Game, which is when they learn of the Professor's silent benevolent witness.