The longish imprint on Hoyle's Games Improved, revised and corrected by Charles Jones Esq. (1814) lists twelve booksellers:
- W. Lowndes
- Wilkie and Robinson
- J. Walker
- Scatcherd and Letterman
- Longman, Hurst, Rees, Orme and Brown
- Lackington, Allen and Co.
- W. Stewart
- B. and R. Crosby
- J. Richarson
- J. Mawman
- J. Asperne
- R. Baldwin
While I can't establish how Gale came to acquire a share of the copyright, nor why he wasn't on the imprint, I have found records showing that not only did he own a share of Hoyle in 1814, he bought a second piece in 1817. Records also show what happened to those shares.
In the 19th century most of the booksellers trade sales were run by the auction house Hodgson and Co. The catalogues for these trade sales, often annotated with purchaser and purchase price, survive. [See One Hundred Years of Book Auctions. 1807-1907. Being a brief record of the firm of Hodgson and Co. London. 1908. pp19-20, available for download]. Copies of the Hodgson catalogues are available at the British Library, as described here (search for "Hodgson trade sales").
A Hodgson catalogue for May 2, 1817 shows Walker, a name from the 1814 imprint, selling a 1/72 share to a name that seems to read Gale & Co.
Researching Gale in the British Book Trade Index, and WorldCat, I found that Gale did business as Gale, Curtis, and Fenner from 1812-15, and as Gale and Fenner from 1815-1817. Fenner succeeded to the business in 1817, and was not terribly successful, becoming bankrupt in March 1819.
Hodgson auctioned Fenner's copyrights on August 10, 1819. There were two lots of the copyright of "Hoyle's Games by Jones", one for a 1/24 share (the share recorded in the Longman Archives) and the other for a 1/72 share (the May 1817 purchase).
It is unclear whether the lots sold at the August 1819 auction--there is no annotation showing a purchaser or purchase price. It is likely that Whittaker acquired the shares either at the auction or later--the Longman records show that he owned none of the copyright in 1814 and a large 11/36 share by 1820.
So, Gale DID own a share in 1814 despite the absence of his name on the imprint. He acquired more in 1817. His successor Fenner sold the shares, apparently in connection with his bankruptcy.
Another minor mystery if not solved, then certainly clarified.