The paper is inappropriately titled, it doesn't prove at all what it claims. Dark matter, or rather Non-baryonic matter, is by definition different from the ordinary matter observed anywhere on earth, and the paper does nothing to prove the existence of such matter.
It actually proves something quite different: that in the case of this particular pair of colliding galaxies, the greater part of the mass is associated with the galaxies and not with the hot intracluster gas. This evidence is that gravitational-lensing measures of total mass outline the concentrations of galaxies, which are physically separate from the main hot gas concentrations.
So, how do Clowe et al get from what was actually indicated to what they claimed? Only though a big assumption, which is in no way supported by their data.
The major assumption is that all of the baryonic, ordinary matter is in the form of hot plasma or bright stars in galaxies. The paper shows that the total amount of gravitating matter, as measured by gravitational lensing, does not correlate with the amount of hot plasma, as measured by x-rays. Therefore, the authors argue, the gravitating matter is instead associated with the galaxies. Since the gravitating mass is much greater than the mass in easily-visible stars, and by assumption, there is no other baryonic matter, the mass must be non-baryonic or dark matter.
The flaw in this argument is this assumption that all the ordinary matter in galaxies is in easily-visible, bright, stars. Instead, most of the mass of galaxies may well be in the form of dwarf stars, which produce very little light per unit mass, in other words have a very high mass-to-light ratio. Several studies of galaxies using very long exposures have shown that they have 'red halos', halos of stars that are mostly red dwarfs. Other studies have indicated that the halos may be filled with white dwarfs, the dead remains of burnt-out stars. In addition, there is evidence that a huge amount of mass may be tied up in relatively cool clouds of plasma that do not radiate much x-ray radiation, and would be in closer proximity to the galaxies than the hot plasma.
The Clowe papers in no way contradict these possibilities, so in no way prove the existence of dark, or non-baryonic matter. Instead, they assume that any mass associated with the galaxies that is not in bright stars is non-baryonic, dark matter.
They assume what they seek to prove.