The shot of the staircase leading to this room gives the audience an understanding of what is happening in this scene. The Ambassador and Cliff are sitting at the control panel listening to a conversation; supposedly between Houston and Armstrong. But the camera reveals by showing the staircase that leads from where the Ambassador and Cliff are sitting, down to a small room at the bottom on the right are Al and Mitch faking this conversation on walkie-talkies. Al is pretending to be Houston telling Neil Armstrong the stastics and readings while Mitch being Armstrong would reply with “copy that” each time, simply convincing the Ambassador that he is listening to a real Armstrong and Houston conversation.
The shot of the staircase also reveals the position of which each character is located in this scene. In the beginning the camera shows Cliff and the Ambassador at the control panel and Glenn in the background, the camera then cross-cuts over to a shot of the stairs, the camera slowly moves down these stairs to a room off to the right where Al and Mitch sit with their walkie-talkies. The Ambassador has no idea that Al and Mitch are sitting right beneath them faking the conversation he listening too.
I believe that what the director was trying to achieve with the shot of the staircase was to give a better understanding to the viewers of what is happening in this scene and