Why is the article titled "Newton's law of gravity passes its biggest test" if it doesn't explain the movement more than MOND?

Other way around. Newtonian dynamics explains the data very well, MOND did not.

In particular, Newtons law of gravity says the effect of gravity falls off as 1/r^2 where r is the distance from the mass. MOND modifies the standard equations so that gravity starts like 1/r^2 when r is small, and acceleration is large, but for greater distances, when the acceleration is low, instead falls off like 1/r.

MOND explains the movement of the stars in (most) galaxies very well. However this result showed that MOND was not consistent with the motion of the galaxies in the cluster. On the other hand the motion was consistent with plain Newtonian dynamics. Hence Newtons law of gravity (and by extension GR) passed the test.