Games are fun. They allow persons to be engaged in another world, however, long or short that time might be. Let us look at some social motivations for game playing.
Gamers usually gain new ideas from a collaborative effort. Many minds come together on a particular topic and a problem may be able to be solved more strategically or faster when everyone gives a response to the challenge/task at hand. Once discussions are held, the best solutions can then be decided upon.
All games have some kind of incentive and give points and/or other rewards for achieving goals set out in the game. Many, if not all, players are driven to get ahead of the next person, level-wise, on the ranking table while they strive for the current incentives at a particular level in the game.
In a game, if someone attacks, it may very well spur you on to prepare a counterattack. If other players assist you in some way, you may want to return the favor.
When playing games, many game designers offer areas in the game or maybe use some social networking facility to allow players to share the experiences they had, strategies they used and other gaming tips and tricks.
Socializing & Networking
Most games call fellow players, friends. And so they are. They may not meet around a social topic, however they still relate to persons and possibly gain opportunities to make new friends through current friends.
Here is the link to a video that summarizes social motivators in gaming. (It runs a bit quickly so you may want to pause it where necessary.)