In a multiplayer boardgame or card game, the focus is on who (which player) you're going against, not on how you're getting there (maneuver). In a two player game, the focus is on how you're getting there, not on who you're going against, because there is no choice of the latter (you have only one).
In general, in non-electronic games, in multiplayer games you're playing the player much more than the "system". In electronic games, even multiplayer, you're playing the system first, then the other players. You can't "look them in the eye", you can't see body language. Yes, you can use Skype or some built-in system to talk to your opponents, but you may not KNOW them, and you won't see them. It makes a difference.
Do people who play as opponents in online multiplayer electronic games become friends? I'm not talking about co-operative games like Everquest, where they're in the same party/guild. I think the answer is no. Do players of multiplayer non-digital games face to face become friends? Often, if they aren't friends already.