The link is to "Stemmata Shirleiana"
On p 22, it says "By a fine of the manor of Eatendon levied in the 10th of Edward II, it would seem that this Ralph was not the son of Sir Ralph Shirley by Margaret Waldershef his wife; he was probably, therefore, a son of a former marriage, as he undoubtedly succeeded Sir Ralph as head of the family ..." His wife was the one known as Isabelle de Eatendon, NOT a Margaret. I think there is a note referencing such a person in W-2's profile.
Apparently the younger Ralph was supposed to have died without issue, so the estate went to half-brother Thomas, son of Ralph and Margaret.
At the beginning of the book is a pedigree showing the 2nd Ralph.
He cites "Dugdale", but Dugdale's Antiquities does not mention this 2nd Ralph. (ETA: Yes, it does.) The Visitations of Leicestershire and Sussex don't mention him.
Also, on Genie, there is a listing for a "Ralph Jr" that cites someone called Nichol, which I haven't seen.
I think this account is sufficiently reasonable as to deserve investigation.