As NBC and CBS began using the NTSC color standard in 1953 and 1954, there were a number of instance where they aired a single episode of a series, or brief string of episodes, in color. It's fascinating to look at the "Colorcasting" sidebar in Broadcasting magazine from the mid-1950s and see how diverse the networks' efforts were.
As noted in Broadcasting, game shows were aired in color (or were planned to be aired in color) on at least the following instances in 1954:
Feb. 9: Judge for Yourself (NBC)
Mar. 15: Name That Tune (NBC)
Mar. 19: On Your Account (NBC)
Aug. 25: The Big Payoff (CBS)
Sep. 19: What's My Line? (CBS)
Oct. 23: Two for the Money (CBS)
As the year went on, NBC began concentrating on color inserts for "Today" and "Home" and its big-budget primetime color series. CBS continued to experiment, even airing some of its daytime serials in color: "Love of Life" on September 8, "Search for Tomorrow" on November 17, "Valiant Lady" on December 1 and 2, and "The Guiding Light" on December 30.
I haven't had the chance to go through 1955 and 1956 yet, so there might be more surprises lurking. Thus far, it appears that the first game shows regularly aired in color were the primetime versions of "Tic Tac Dough" and "The Price is Right" beginning in September 1957.