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Most of those you could probably play with modern integrated graphics (Intel HD 3000 / AMD APUs) albeit on low settings. For some of the FPS games like Nexuiz or Sauerbraten you'll definitely need a dedicated card to play without lag on anything other than the lowest settings.
If you'd need some comparison, on my T500 with integrated graphics (GMA X3100), Urban Terror, Tremulous, and BZFlag are all quite playable at their maximum quality settings, and Nexuiz runs well at low/medium settings.