Before proceeding, it should be mentioned that the statistical significance of the result is still under debate. While the asymmetry is significant at the ≳3σ level, some question whether it is simply a consequence of the “look-elsewhere” effect: i.e., we test for all kinds of anomalies in the CMB, and the investigated parameter space is so vast that it’s no surprise that, by chance, one of the parameters shows a positive result. Cosmological models make statistical predictions about the distribution of temperature fluctuations on an ensemble of CMB skies, but we have only one CMB sky to observe. Therefore, if the observed asymmetry is a statistical fluke, we are stuck with it because there is no way to increase the statistics on this particular measurement. But if the asymmetry is real and not just a statistical fluke, then it is extremely important. It may well be a remnant of the preinflationary Universe!
The dipole anisotropy in the power spectrum seems real (not the doppler dipole, but rather the one discussed in these articles). Alright, that's out of the way. This observation needs to be interpreted to get any further, though.
One possibility is that this is just a $3\sigma$ excursion from the expected isotropy. Without a statistical sample of additional Universes to observe, we have no way of knowing for sure. And as the article points out, if you look at enough parameters, eventually you'd actually be surprised if you didn't find one off by a couple of $\sigma$.
Another interpretation is that the Universe is a little bit curved (in the "Open" direction, i.e. negatively). This depends on the model some theorists are proposing being at least broadly correct. However, for the moment, this class of models offers no other presently testable predictions. I'm sure the theorists are working on more predictions that are testable, and CMB observers are working on measuring the predictions that have been made (the signal is supposed to be very faint, and the measurement is very difficult). But for the moment no other tested predictions means that this is just another class of theories, and there is no compelling reason to prefer it over the usual flat Universe model. In fact, I would prefer the flat model as it has less parameters and also explains the observations (even though I have to live with a $3\sigma$ statistical anomaly).
The same article also mentions that the anomaly is seen in the two hemispheres roughly separated by the ecliptic, which is somewhat worrying. Alignment with the ecliptic, or galactic equator, or other preferred direction, to me is suggestive of some uncorrected systematic effect. Not to say that this can't be a real anomaly because it's aligned with the ecliptic, but it's worrying...
So to sum up, there doesn't seem to be any compelling evidence for an open Universe. There is this anomaly in the isotropy of the power spectrum, but it's not so large that it couldn't just be happenstance. If the proposed curvaton model makes some additional predictions (differing from the predictions of the usual cosmology) that are later borne out by observation, that would be more strongly suggestive of an Open geometry.