I would also bet that getting the game to perform the exact same series of allocations would be an intractable problem to solve. I don't think Doom 3 has a benchmark mode; the author just recorded themselves loading the game, loading a level, doing a bit of gameplay, etc.
Carmack is a great empiricist, meaning he pays a lot of attention to how things work in a running system. All of his engines provide rich facilities for record and replay as well as running benchmarks.
There are lots of facilities for recording and playing back demos. The author could record their own gameplay and play it back in realtime vs running timedemo (which plays back as fast as possible).
id Tech games have "timedemo" mode, where they replay a pre-recorded demo as fast as possible, and report how many FPS it was able to process. These were very popular benchmarks long ago.