You do clarify it in your post, but I think you should probably make the overall question a little bit clearer.
IF a game was conceptualized, developed, advertised to be and really is just a multiplayer experience, there isn't anything wrong with that. Games like Team Fortress and Counter-Strike,, Tribes, League of Legends,, and, hell, really the entire MMO genre exist in terms of the content they provide for communities as a whole, not single gamers. (Yes, you can play MMOs alone to some degree, but the experience, I've found, is never as enjoyable).
Yahtzee's problem is with games like Call of Duty and Battlefield, where the single-player campaigns have become almost woefully short, and the real effort is clearly put into the multiplayer modes. This is the problem. A game that contains a single-player experience but is clearly selling itself on the multiplayer side of things is, in a way, a terrible lie. If a game contains a single-player story, then it alone should justify the price tags. If you were to buy a (recent) Call of Duty, Battlefield, or Medal of Honor game (really anything that can be fit under the classification of 'spunkgargleweewee,'), and only be interested in, or have access to the single-player, you'd be extremely disappointed.
THAT'S Yahtzee's issue. He's professed his enjoyment of Team Fortress quite a bit, so it's obvious he's not adverse to multiplayer as a concept. Just in its recent manifestations. That's a problem he has with the Borderlands games, as well: yeah, you can play the game alone, but everything about its design is pushing toward multiplayer. And then, when you do play in multiplayer, its just the same game with three more people running about, and a slight increase in difficulty. Single-player and multiplayer should be two distinct, equal entities in any game where both are contained.
So, I suppose, in answer to your question, yes, a game must stand on single-player alone, assuming that it includes one, and is suggesting that it alone would justify the cost of admission (which all multiplayer games still do, even though we all know better by now).