A RPG/FPS style game would suit, Gamers could be Timelords, Soldiers or Pilot, It could have all sorts of threats over a wide universe, Quests and Missions and a different style of combat for each class.
It could work online or off, And have it like a Historical reflection of the Timelords, Being able blast Daleks and Cybermen with Ub3r weapons with the Soldiers.
The Timelords would have the advantage of a radar and a slight speed increase, But they would not have many attack options, making you use your cunning and stealth advantages.
Pilots would be Tardis crew and have good weapon skills, And also Engineer and Medic skill sets.
And for the Timelords death would mean regeneration and a change in your abilitys and a more puzzle solving style of play.
I would play it