...be disgrammed like this:

2nd Sir Walter -> elder (only?) son -> current Sir Walter (elder son)

2nd Sir Walter -> elder (only?) son -> younger son (brother to Sir Walter) -> William Walter Elliot (great grandson)

This does make William the nephew of Sir Walter, but I agree, the text is not specific about this. I wish I knew what prompted Dr. Chapman to say Mr. Elliot is the "nephew" - unless there wasn't as strict an interpretation of the word "nephew" then, as there is now.