The debut game Thursday, featuring the Pittsburgh Steelers at Baltimore, was eliminating a track of Jay-Z's "Run This Town" featuring Rihanna, McManus said. Other "high-energy" elements and a comedic one also were being dropped.
The changes were made to give the game coverage a more "subdued" tone and journalistic approach, McManus said.
The broadcast was to open with a report by CBS News' Norah O'Donnell about Rice, who was cut by the Baltimore Ravens after TMZ released the surveillance video Monday.
The footage has called into question how the NFL disciplines players involved in domestic violence. Earlier, Rice had been suspended for two games for the assault.
Asked if Rihanna's own history as a victim of domestic violence was a reason the song was cut, McManus said it was among several factors considered but was not the overriding one. Rihanna was attacked by then-boyfriend Chris Brown before the 2009 Grammy Awards.
How the network will approach next week's broadcast has yet to be determined, McManus said.
CBS Sports had previously announced that "Run This Town," with added narration by Don Cheadle, was to accompany each of the 2014 broadcasts as part of an opening sequence that would be customized for each week's game.