Personally, I dont. I dont even care who's in a lobby with me, let alone if they are on another system. I rarely play multiplayer games anymore, aside from some occasional deathmatches. My collections are mainly single player games and RPGs. Online shooters get boring so quick nowadays.
People can be addicted to anything. Games, drugs, working out, buying things, gambling, etc. It comes down to the individual and the strength of their mind.