I think there is an important part of the answer missing here. Most of the answers tell you to "Know your data". The fact is that you must, in the same way and with the same degree of importance, also know your:
- CPU (clock and caches)
- Memory (frequency and latency)
- Hard drive (in term of speed and seek times)
- GPU (#cores, clock and its Memory/Caches)
- Interfaces: Sata controllers, PCI revisions, etc.
BUT, on top of that, with the current modern computers, you would never be able to player a real 1080p video at >>30ftp (a single 1080p image in 64bits would take 15 000 Ko/14.9 MB). The reason for that is because of the sampling/precision. A video game would never use a double precision (64bits) for pixels, images, data, etc..., but rather use a lower custom precision (~4-8 bits) and sometimes less precision rescaled with interpolation techniques to allow reasonable computation time.
There are other techniques as well such as Clipping the data (both with OpenGL standard and software implementation), Data compression, etc. Keep also in mind, that current GPUs can be >300 times faster than the current CPUs in term of hardware capability. However, a good programmer may get a 10-20x factor, unless your problem is fully optimized and completely parallelizable (particularly task parallelizable).
By experience, I can tell you that optimization is like an exponential curve. To reach optimal performance, the time required may be incredibly important.
So to get back to the teapot, you should see how the geometry is represented, sampled and with what precision Vs see in GTA 5, in term of geometry/textures and most important, the details (precision, sampling, etc.)