From "Rhind Papyrus" from 1600 BC we know that the Egyptians had an estimate for pi, namely 3.16, meaning they knew only 2 digits of pi. According to this article they knew more digits, at least 4 digits of pi. Around 200 BC Archimedes estimated pi to 22/7 which is 3 digits of pi. This indicates that the Egyptians knew more digits 2000 years before Archimedes, however, it's not clear to me how many digits they actually knew.
The ancient Egyptians at the time of the Rhind Papyrus didn't really have the concept of Pi. The method they described for finding the area of a circle was to inscribe it within a square, and apply the ratio of 64/81 to the area within the square. However, we know today this is mathematically equivalent to using a Pi of 256/81. That's a hair smaller than 3.1605, which on Wikipedia's timeline page amounts to having it right to one decimal place.
The Ancient Babylonians and Indians at roughly the same time had their own heuristics which worked out to a Pi of 3 + 1/8 and 25/8 respectively, or 3.125 (exactly). That was a wee bit closer, but also accurate to only one decimal place. Nobody else is known to have widely established a significantly better estimate until Archimedes' 2 decimal places nearly 2000 years later.
The paper you linked is making several speculations and extrapolating from them. I don't wanna give the guy short shrift: they are some fascinating speculations. I find the idea of the pyramid builders rolling around a trundle wheel to plot out the four corners particularly compelling. But at its base that paper is just a lot of personal speculation and math fun, built around a core of historical and mathematical fact. It is of course quite possible to be using Pi without knowing it; that's exactly what our trundle wheel users would have been doing.
There was an Egyptologist who argued as early as 1940 that the Egyptians were also using 22/7, but that argument does not appear to be widely accepted today. I'm not sure how closely his arguments match to the paper you linked.