The fluctuations seen in the CMB are predicted by inflation -- only classically do we expect inflation to furnish a perfectly homogeneous universe. Inflation is expected to amplify and stretch quantum fluctuations in the inflaton field which come to manifest themselves as temperature/polarization fluctuations in the CMB. The discovery of these temperature anisotropies by COBE in 90's (way before Planck) is actually considered to be some of the first evidence for inflation -- not against it. By studying the properties of these fluctuations, e.g. their power spectrum, we can learn much about the physics of the inflationary era. So, no. Far cry from killing inflation: the inhomogeneities are a consequence and vindication of the inflationary proposal.
Now, in the article they also talk about certain large-scale anomalies seen by Planck. Indeed, these are a challenge to the simplest realizations of inflation. But, they are by no means a death knell. If they are indeed of primordial origin -- a fact that is not currently known -- then we will need to consider more complicated forms of inflation, for example, ones that involve a breaking of isotropy through vector fields.
