This result is extremely narrow and does not offer any generality. In the specific problems space the researchers attacked they did not find that quantum computers were better than classical computers. What they state in the paper is something far more specific and thus less powerful. The comparison is between a 2D quantum grid of 1 qubit and 2 qubit gates versus a classical (probabilistic) circuit. They found that in the classical (probabilistic) circuit there is a strong lower bound on the depth of gates required to solve the problem (log n, where n is the size of the input). In the quantum grid case the depth remains constant as the computation is carried out over a 2D quantum grid.
Both Science and other write ups about this result, including this post, seems to paint this result very generally and it simply isn't. It's not an algorithm, the paper does not pit quantum vs classical computers, simply circuits. There is no analysis as to the size of the quantum grid required w.r.t. the size of the input, only the depth of the circuit. Also by leaning on probabilistic classical circuits they move the goalposts into an exotically small portion of the problem space.
The result is rather great, but it is nothing like the media is portraying and it is not a general result at all. Please don't take the above as anything other than media critique and clarification of the results in the paper.