The basic idea here, is that the reference frames used to measure galaxy rotation curves may not be inertial. that is, they might be influenced by rotational or other accelerative forces due to the galaxies' motion in the universe. Traditionally, it's assumed these frames are inertial, meaning they are free from such influences, which simplifies calculations but might overlook significant effects, and that's the key point that has been missed and is addressed by the paper, showing that you can't overlook those effects.

if we consider these non-inertial effects akin to acknowledging that galaxies might not be moving in straightforward, stable paths but could be "flying around" each other or a common center, then we can account for the observed rotation curves differently. They suggest that the forces arising from these complex motions could mimic the effects attributed to dark matter.

AFAIK, this has not been rigorously checked in the past. However, there are several other phenomenon that are explained by dark matter / dark energy besides this discrepency, so people in the field are not very eager to give up on dark matter just yet