That's reasonable critique on multiplayer-games. Basically, the main objective switched from teamplay to "Look at me, I am the best and the rest of you are noobs!"

However, that doesn't apply to offline-multiplayer. When I grew up, I hadn't access to online-PC-games, but PS1 only. Back in those days multiplayer meant to sit together in one room, talking to each other and playing with 2 controllers. There was no rushing through, but cooperation was necessary to accomplish certain goals. Also it was limited to 2 players (maximum 4 with an adapter).
Some games I remember playing (coop and competitive):
Hogs of War / Frontschweine(ger) (2000) - A delightful turn-based strategic game, similar to
Worms Armageddon (1999), except in 3D. The Theme was WWI (or maybe WWII, I don't remember), packed in great humor and a lot of challenging campaigns for single player, too. I know, the graphics don't look very promising, but the gameplay is excellent.
Crash Team Racing (1999) - Probably most people would disagree, but in my opinion it's an strongly improved version of
Mario Kart 64 (1996), but featuring characters from the Crash Bandicoot series. I had a lot of fun playing it with friends.

It's quite popular though, and not really worth mentioning, since most people do know this game.
Herc's Adventure (1997) - Neat game, both witty and challenging. It had a few flaws, but overall a game worth playing. I never finished it though, because game-breaking glitches started to occur. I assume the CD got scratched by accident

(Couldn't find a proper image)
Also
Legend (1998) - It was not that great (or maybe I was just too bad?), but still entertaining on multiplayer.
Diablo (1996) - One of my favorites. Back then it was very difficult, since some gamemechanics weren't very clear, neither to me, nor to my friend. Nevertheless we finished it somehow by using the weirdest strategies ... Oh, those times.
Fighting Force (1997) - Same as Legend, too repetitive and quickly boring, but stil enjoyable with friends fooling around with enemies. ))
Every game mentioned was for the PS1, by the way. That's the only console I ever had (besides a Gameboy with 4 or 5 games).
Mert, this is how GTA looked like, when I used to play it
Grand Theft Auto 2 (1999)