Who or what is the antagonist in The Egypt Game?
This is an interesting question, as in a sense, there could be said to be many different protagonists. At the end of the novel, however, we discover that the main protagonist who has been responsible for the murders of the children and the failed attack on April is not actually the man that we and the children had expected--the Professor--but it was actually somebody completely different:
He was a relative of Mr. Schmitt and he had always had something wrong with his mind. He couldn't get a good job, and sometimes Mr. Schmitt let him work as a stockboy in his store. He's work for a while and then he'd go away and do something else. But he always came back again, and since he was willing to work for very little money, Mr. Schmitt always hired him again.
So, whilst the ginger-headed man is clearly the principal protagonist, if you want to think a bit more metaphorically, you might want to consider how actually a major protagonist is fear and prejudice of those who are different from us. The children suspect the Professor of committing the crime because he is such a recluse and so strange to them. An important part of the novel is their realisation that being different does not mean that you are responsible for crimes. They grow and develop as they make this realisation.