Through hypothesis testing you can estimate the probability that this was due to luck is very low. Assuming that a monkey would have a 50% chance of profiting on a day, the chance of going a month without a losing day is less than 1 in a billion.
I very much look forward to the author's follow up post at the end of 2020 to see if another 5k turns into 200.
The number of monkeys required to match the author's results over a 12-month period is well over the number of atoms in the universe.
On the other hand, if we wanted to test his 3900% yearly return, we might assume that monkey returns are equal in distribution to Bitcoin's price and then test the hypothesis that he's a monkey via something like a paired t-test. The problem here is that we only have one data point so p-value is undefined, and due to high variance it would probably take about n=10 points to get something significant. The upside of this approach is that you can get a confidence interval for how much better he is than a monkey, instead of just a yes/no answer.
In any case, since the author has at least 365 data points, he probably has an extremely good idea of both a) whether he's a monkey, and b) how much better he is than a monkey.