It is the performance win for similar looking results that I find improbable. For a box blur to look like gaussian blur, you would need multiple passes. Even though each pass is now O(1) instead of O(n) (with n the blur radius), due to caching effects I think a gaussian kernel would still be faster, especially for the small blur radius as described in the article.

That link is not a box filter, as it still uses weights to approximate a gaussian convolution kernel. It just uses some special hardware to do less texture fetches. But that is a constant 2x improvement over the full 1D convolution, not the box filter O(1) approach that the article suggests that browsers are using.