It's a bit unfair to ascribe it to sheer luck. They were focused on the compute related possibilities all the way back with the GeForce 3 in 2001. Presentations from its launch were already talking about the potential of a "parallel compute monster" [1].
They saw the potential of GPU compute very early on, invested in it long term and as a result eventually ended up dominating the market. The others didn't seriously commit and so they fell behind. AMD still can't seem to commit, while Intel seems to be working hard on catching up but isn't quite there yet.
The actual quote from your link is: "Expect a massively programmable, massively
parallel and pipelined graphics monster", not a "compute monster".
While I agree that Nvidia positioned themselves well, they were not looking as far forward as you suggest. As I recall it, they seemed surprised by BrookGPU, though they moved quickly to embrace the model.
They saw the potential of GPU compute very early on, invested in it long term and as a result eventually ended up dominating the market. The others didn't seriously commit and so they fell behind. AMD still can't seem to commit, while Intel seems to be working hard on catching up but isn't quite there yet.
[1] https://developer.download.nvidia.com/assets/gamedev/docs/GF...