I think what we have here is a failure to communicate.
In my view, DND is a zero sum game. (Sit down in the back, let me explain!) However, the conventional model of 2 groups at the table is flawed IMO.
There are not two groups at the table, players and DM, there are three: Players, DM, and Challenges. Each group is fundamentally playing to different win conditions so that, even though someone is going to lose, it is very possible for two groups to win.
For players to win, they overcome challenges. I don't think anyone would disagree with that. It is very rare that individual players overcome challenges rather than the party as a group. Granted, individual players can fail to overcome a challenge (ie. die), but, generally, parties work as a group.
For DM's to win, its a little more subtle. In my view, DM's win best when the players fully engage his creation and treat it as "real". The more the players engage in what the DM sets forth, the more the DM wins.
The third group is the challenges. Now, challenges are created by the DM, that's true, and, to some extent, controlled by the DM. However, the DM has no vested interest in seeing the challenges win. And, the DM has (or should have) no ability to ensure that the challenges foil the party. While the DM can certainly have that troll attack that PC, he cannot dictate the results of that attack. To a fair degree, the challenges have autonomy separate from the DM.
However, when all is said and done, it's the challenges that most frequently lose. But, since the challenges have no existence, we don't care. We don't pause and wonder if Joe Orc is truly enjoying the ass whupping he's receiving from the party. Why would we?
Everyone plays to win. That's true in any game on the planet. All games, by their very nature are competitive. However, the mistake in this case is trying to say that the players are competing with eachother or the DM. They aren't. They are competing against the challenges. If they defeat the challenge, they have fun. If they fail to defeat the challenge, their fun is less. Fail to defeat any challenges and the players have no fun at all.
DM fun is a lot more slippery to pin down. I liken it to the fun a referee has during a game. While the ref certainly isn't playing, that doesn't mean that he's not having a good time.