I misread the article the first time. That's a fair way to estimate pi.
Consider a square with side of length B with a circle of diameter B drawn inside.
The area of the square with the circular area removed is B^2. The area of the circle is pi(B^2)/4. Their ratio reduces to 4/pi.
Example with B = 7 inches -
The circle's area is 38.48451 in^2. The square is 49 in^2.
49 / 38.483451 = 1.27327 = 4 / pi exactly.
Another way to approximate pi by this method is to shoot at a circle with a diameter drawn. Count the number of pellets on the diameter and the circumference. Divide the number of pellets on the circumference by the number on the diameter to find the value of pi from its fundamental definition.
The interesting experiment would be to count pellets from one shot, then two shots, and so on until you're tired of counting little holes, and watch the approximation converge on pi.