President Bartlet's answer about the death penalty during the cold open is taken (almost verbatim) from the answer Governor Michael Dukakis gave during a 1988 presidential debate against then-Vice President George H.W. Bush. Dukakis was asked if he would support the death penalty in the event that his wife were raped and murdered; he responded almost identically to the President's faux answer. The response from the public was exactly as Toby said it was: barely human.
The bar where Sam meets Will Bailey in Laguna Beach is called The White House.
This episode marks the first appearance of Joshua Malina in the West Wing. He previously appeared in all episodes of Aaron Sorkin's Sports Night (1998).
The character of Will Bailey's half sister is named "Elsie Snuffin". This is a reference to real life actress Elsie Sniffen (who later changed her name to Kayla Blake), who had a recurring role as Kim in Sports Night (1998), also written and created by Aaron Sorkin. Executive producer John Wells was also a supervising producer on the series China Beach (1988), where Sniffen appears in at least one episode.
Ben Travers, writing for IndieWire, briefly touched on "Game On" as part of a list of "15(ish) Episodes of 'The West Wing' To Binge View In Celebration of America", released in commemoration of Independence Day.