Thank you, Walter, for that very stimulating question.
The test you are referring to is a test to predict VO2max (maximum oxygen consumption, tested under maximum stress test, in this case on a treadmill).
As far as I can see, the website you referred to does not offer a test for estimating biological age based on fitness levels.
But they offer a fitness calculator. I follwed through, and here is what I found.
The data is from the HUNT study performed in Norway on about 37,000 men and women. (have been aware of these data since along time, because they contain a wealth of information).
VO2max is a very strong predictor of morbidity and mortality, hence it is an important biomarker for biological age. Now, there are two issues that you have to keep in mind. First, VO2max is not a perfect predictor of premature death and disease (no biomarker is perfect, fortunately). Second, the algorithm that the researchers developed is, and I quote them, "The nonexercise regression model developed in the present study was fairly accurate in predicting V˙O2peak in this healthy population of men and women. " When researchers say "fairly accurate" it certainly does not equate what the website you quote says "Estimates fitness accurately". The algorithm explains 61% and 56% of the variance in VO2max for men and women respectively. That is, roughly 40% of the population variance are NOT explained by their algorithm. That is no surprise, because only age, BMI, resting heart rate (RHR) and self-reported physical activity made it as predictors. So, if you want to use this relatively incorrrect prediction as a basis for age prediction, you'll end up with a prediction that will not be any better, but rather worse.
That is not to say that the HUNT prediction is useless. On the contrary. I quickly ran the numbers of one of their studies in which they predict CVD mortality using their VO2 predictor formula. If you were to take the low fitness category as predictive of mortality, you'd have a predictive accuracy of 30%, that is, of all those identified as of low fitness one in three would die prematurely (from CVD). The risk of dying prematurely if you are NOT in the low-fitness category is roughly 10%. So you have a 20% absolute risk reduction. That translates into a number needed to treat (NNT) of 5. That is, if we were able to convince those in the low-fit group to do more exercise, thereby increasing their fitness level, we would need 5 successes to prevent one case of premature death.