Out of my own collection, I found non-sports games that do not feature any kind of death:
Animal Crossing, Ape Escape, ARMS, Billy Hatcher, Bust-a-Move, DDR, King of Fighters, every single Mario Kart, Luigi's Mansion, Professor Layton, Puyo Puyo, Rhythm Paradise, Rumble Roses, Samba de Amigo, Super Smash Bros., Tetris, Warioware.
These games exist, they always have, they just may not be as popular as CoD
I also found a couple of games that would practically be ruined without the concept of life and death in place:
Fire Emblem, Pikmin, Trauma Center (The Sims? maybe??).
Meanwhile Crash Bandicoot can 'Die', he has a couple 'Death' animations which do not involve a death.
Even Cel Damage makes a joke that they're all cartoon characters, so they never get injured.