Dead player's line of sight tracks his killer
From DoomWiki.org
When a marine is killed by a monster or another player, his field of vision (as seen on the player's screen) rotates to face his attacker. If that attacker continues to move around, the dead player's field of vision continues to follow him for an indefinite period in response.
This feature normally goes unnoticed during deathmatch play, since it is prudent to respawn as quickly as possible.