This isn't an estimate, it's an upper bound. Unless I've missed something, a board filled with 2s would be counted as possible by this article, despite being unreachable. There are many unreachable states that they are counting.
The article doesn't even make an argument that it's close to accurate, though. It could be off by several orders of magnitude, and whether it might be or not isn't even discussed!
On the other hand, it is giving an exact upper bound; it's a proof that the actual number couldn't be any larger than 44 quadrillion.
Last paragraph in the article: "In the next post, we’ll see that the number of actually reachable states is much lower by actually enumerating them. There will still be a lot of them for the 3x3 and 4x4 boards, so we will need some computer science as well as mathematics."
