In John's theology, the world is anything that rebels against God. So in Scriptures most quoted verse (John 3:16 "for God so loved the World that God gave God's only begotten Son, for whoever believes in him will not perish but have eternal life.) God so loved the world....this world, the world that rebels against God....God sent God's Son to redeem that very world.
I say that because their is way to much happening in the world around us right now to realize that a simple defection from the world by Christians doesn't work. Not if we are to take this commandment seriously. Nor does an imposition of the churches values upon the world create living into loving your neighbor.
Engaging in the love one another command from Jesus is easy when we know and assimilate into a homogeneous society. BUT this comand hits the ground running when when hear the blessings of the kingdom that Jesus reminds his disciples....."Blessed are you when people revile you because of me....Blessed are you when you are persecuted because of believing in me."
Jesus can say those things because in the grand scheme of things the things of this world are temporary until Jesus returns to make all things new. Therefore, John invites his community (and us) to love one another especially when the world rejects that love in order to bring the kingdom into a broken and hurting world.