In this scenario only you can be considered as your team, and everyone is your potential enemy, whose you should eliminate as fast as possible. In this paintball scenario last man standing or kill leader wins.
There is also team deatchmatch altenative scenario which assumes spliting the group into small teams.
Deathmatch is a reasonable choice for players wanting to improve their movement and shooting abilities. In this scenario you can become a individualist – a hero who will give other players a hard time.