Well, it was also known to be fake trickery. But fake trickery that ran fast and looked good.

IIRC Quake 3 levels had true curved surfaces, though presumably they were polygonised at some point in the rendering pipeline.

They were dynamically tessellated on the CPU. These days we can of course do the same thing on the GPU, using tessellation/geometry/mesh shaders or even compute shaders, depending.