Doom 3 wasn’t necessarily the first game with fully-dynamic lighting/shadowing, but it was among the first to use what Carmack referred to as “fully-unified lighting”, in that no pre-baked lighting was used. There were some projection light hacks here and there, but generally speaking all lighting in Doom 3 was dynamic.

The original Quake used a mix of pre-baked lightmaps and dynamic lights, just like the original Thief; Quake 2 (the OpenGL renderer, anyway) added character shadows that’d react to dynamic lights, so in some cases Quake 2 actually got pretty close to the goalpost.