I saw the same episode, and also wondered about the date of those chips. According to Wikipedia, J. D. Borthwick died in 1900, at the age of 76.

Seymour's reprinted list of poker chip catalogs list the earliest mention of inlaid chips is 1895, and of initialed inlaid poker chips in 1900.

What makes the association with Borthwick more dubious, is that according to Wikipedia he was in the US in the 1850s, and returned to England in 1857. He was also a travel writer, who happened to gamble playing cards, rather than a professional gambler.

So this kit may either have belonged to a professional gambler from the turn of the century, or is a very elaborate fraud.