> Matter cools when universe expands.More precisely, the energy density of matter decreases as the universe expands.
> Where does that energy go to?
Stress-energy density is locally conserved; there is no energy being created or destroyed. In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with zero pressure) to decrease as the universe expands (as the cube of the scale factor).
> Shouldn't dark energy density also fall?
No, because dark energy, considered as a stress-energy density, includes negative pressure equal to minus the energy density, and the same local conservation of stress-energy density I referred to above requires that in this case, the energy density is constant in both space and time.
Note that the new findings described in the article amount to raising the possibility that what we thought was "dark energy", i.e., a cosmological constant with pressure exactly equal to minus the energy density (that is what w = -1, mentioned in the article, means), is in fact something else whose equation of state (relationship between pressure and energy density) can change over time, with pressure becoming less negative (w less negative than -1). If that is the case, the energy density would also be decreasing over time, though much more slowly than for ordinary matter.