It’s hard to make out the details in those pictures, but we can see that the set decorators at least took the trouble to divide the pieces into correct Axis and Allied camps, with the black German and orange Japanese pieces on one side of the board and the green American, tan British and maroon Soviet pieces on the other side of the board. With four guys playing five powers, the only possible team combination would be two guys playing Germany and Japan respectively, with the three Allied powers split two-and-one between the other two players.
I’ve never seen the show and I don’t know the characters, but from the positioning of the four guys and the five sets of pieces it looks like the two characters on the right are playing the Axis. Their sofa is somewhat awkwardly positioned for both of them to handle the Axis pieces, but it would be manageable for the guy completely on the left to handle Japan (he just needs to get up) and for the guy with the glasses to play German (whose pieces he can reach from his seat). Conversely, it would be difficult for the guy with the glasses to play Japan, since he’d have to lean too far to reach the pieces or get up and walk around the guy who’s on the sofa next to him.
The character completely on the left is probably playing the Russians (the maroon pieces are closest to him), and the character next to him is probably playing the US (the green pieces are closest to him). The British pieces are in between those two guys, so either one could be handling the UK, but the character with the yellow sleeves seems better positioned at the table to control both the tan and green pieces.
So my guess is:
Far left guy: USSR
Middle left guy: Anglo-Americans
Middle right guy: Germany
Far right guy: Japan
It’s amusingly appropriate from a political point of view that (as seen from the audience) the Soviets are on the left, the Germans and Japanese are clustered on the right, and the British and Americans are in the middle.