That is one bizarre story.
I have the British census records from 1881, 1891 and 1901 for Tom Dunn. In 1881 he was living with his wife Isabella, daughter Isabella and his brother William Dunn, otherwise known as Willie Dunn, who was 17 at the time. I'm not sure if Willie was a resident or visiting. In 1891 Tom and Isabella, son John (JD), Son Charles, daughter May, son Seymour, and daughter Norah. In 1901 it was Tom and Isabella, and daughter Norah. Seymour's middle name was Gourlay too, and I have found a couple of Golf Illustrated articles where he was referred to as Gourlay Dunn.
It seems odd that he wasn't living in the home at seven years old. And it is very unusual for a man to change his last name, especially when associated with such a famous family. I'm wondering if W. Chambers was legitimate, which might explain why he wasn't living with his father. Or came from a different father.
The oldest sibling listed on the census records was Isabella, but she was only 10 months. I take it she died prematurely.