For me it's slightly misleading because it's almost like saying "I wrote a faster quicksort implementation, so it beats quicksort!". In this case the binary search fundamental idea of "divide and conquer" is still there, the article just does microptimizations (which seem to be not very portable and are less relevant/applicible for more complex data structures) in order to reduce the constant part.

Yes, algorithmic complexity is theoretical, it often ignores the real world constants, but they are usually useful when comparing algorithms for larger inputs, unless we are talking about "galactic algorithms" with insanely large constants.