I happened to see this thread, being interested in the history. The Wikipedia entry mercifully seems decently researched (Wiki food history entries are notorious: the "purest" bizarre example I've seen was a chicken-salad history there, giving a local newspaper story as the source, the newspaper story in turn citing only the Wikipedia entry).
But the Wiki "King" entry still cites mainly pop-culture sources, and I didn't spot an explanation of why it characterizes one of several stories as "the most likely." For some reason it doesn't quote Ranhofer's Epicurean,
the compendium of Delmonico's recipes from the 1800s. Evan Jones's 1992 essay "Delmonico's," one of two writeups I know with real depth on Delmonico's, mentions the same stories Wiki does, but Root and de Rochemont's Eating in America
(1976, the other in-depth source) states not that Ranhofer "created" it (a claim Wiki mentions in passing) but that the dish did appear on Delmonico's menu
in the 1800s as Chicken à la Keene
(for Foxhall Keene) but slipped into popular culture with a simplified name before it became so widely known (and all those later 1900-era sources that Wiki cites began retroactively looking into the name.)
It's like many other origin ambiguities -- Rueben sandwiches, Martinis. (Conrad's book on the Martini traces three longtime, competing, detailed, credible, utterly incompatible origin stories, each with its unshakable believers.)
Root et al. were contrasting Chicken à la King to the "other" famous Delmonico's chafing-dish specialty that got renamed: Ben Wenberg's "Lobster à la Wenberg" which (print sources are more unanimous here) was retitled "Newburg" by the restaurant after Captain Wenberg, a regular customer, precipitated a brawl there and became persona non grata.