In the simplest terms, relationships established with other gamers expand the space of a particular game by creating a community that exists inside and/or outside the game. The game itself can be a link between people who, otherwise, have nothing in common. Thusly, the game is a vessel that connects people to aspects of human interaction which they may feel alienated or separated from. Of course, the game can also connect people who have plenty in common.
Jane McGonigal would say that games can give people a sense of purpose, perhaps even a sense of purpose that no other part of life can offer. Relationships established with other gamers will add to this sense of purpose by exposing gamers to the unique needs of other gamers. The game is no longer about just playing the game. The game is now also about helping others understand and accomplish tasks in the game. The game does not even have to be played anymore. People can connect by discussing the game, giving them an extra sense of purpose in the non-game world.
McGonigal would also say that the more relationships established with other gamers, the greater sense of awe a gamer has when involved with the game. The feeling of awe is inspiring, and inspired players feel a sense of purpose that is proportional to inspiration. As previously mentioned, the connection forms a community that can be both in the game and outside of the game. Therefore, establishing relationships with other gamers expands the space of a game by giving a sense of purpose to players, both in the game and outside of the game. The game spills over into the non-game world, and vice-versa. The game experience becomes epic, in both realities.