Playing a single game of chess for five hours can be very grueling. Georgi is also one of the first players we've seen Beth play where her win (or loss) wasn't quick. It's also established (I can't remember before or after this scene) that Russian players will use adjournments to consult other players. We're not explicitly shown, but it's possible that Georgi also used his adjournment to consult others for help.
The scene also takes the chance to show us what an adjournment looks like so that when it's used later it's not needed to explain it to the audience.