To unlock these cinematics you must complete a certain chapter of the game:

Cinematic	How to unlock
A Heated Interrogation	Complete Peru
A Tough Choice	Complete Lost City
Ambushed!	Complete Egypt
Arrival at Khamoon	Complete Egypt
Arrival at St. Francis' Folly	Complete Greece
Business Banter	Complete Greece
Croft Manor	Complete Croft Manor
Doppelganger Demise	Complete Lost City
Down But Not Out	Complete Lost City
Final Confrontation	Complete Lost City
Introducing Natla	Complete Peru
Island Arrival	Complete Lost City
Island Escape	Complete Lost City
Kold and Kid	Complete Lost City
Larson Dies	Complete Lost City
Late Night Reccoinsance	Complete Peru
Motorcycle Pursuit	Complete Egypt
Pierre's Demise	Complete Greece
Retrieving the Scion	Complete Egypt
Shadow Figures 1	Complete Greece
Shadow Figures 2	Complete Greece
The Awakening	Complete Peru
The Banishment of Natla	Complete Egypt
The End of the Line	Complete Lost City
The Power of the Scion	Complete Lost City
The Tomb of Qualopec	Complete Peru
The Tomb of Tihocan	Complete Greece
Time to Leave	Complete Lost City
Unexpected Company	Complete Peru
Vilcabamba	Complete Peru
Wolf Attack	Complete Peru