I'd love to know what game or games don't break any of those commandments.
I'd say Halo 2 qualifies. I'm not familiar enough with 1 to make a call either way, and 3 was sort of lackluster story-wise. Probably GoldenEye and Gauntlet Legends (the N64 version), too. If you look to earlier games than that (where "multiplayer" meant "two player splitscreen"), Super Mario Kart (SNES) would make the cut in my book. I'd say Snake Rattle 'n' Roll (NES), but I suppose #5 (don't force repetition/retries) would kill it for most people, as the difficulty was insane and led to a lot
of restarts. Contra (NES) qualifies if you consider that even having
a story was an innovation at that time and let the "aliens attack Earth; two rogue commandos fight to save it" slide.