Objectives in collectible card games
They are not CCGs strictly speaking but Fantasy Flight Games' Game of Thrones Living Card game and the new Keyforge have very different victory conditions.

The latter has Aember, basically victory points, that can be won, lost and stolen. They are automatically used to unlock keys at the beginning of you turn. When you unlock 3 keys, you win. The game still uses, creatures, artifacts and instants, but all serve to earn Aember.

Killing creatures only slows your opponent down. I like this system a lot!