and it is legit, but it is pretty routine astronomical stuff. The blueshift discussed is not of cosmic significance (i.e., it does not call into question the Doppler effect) but describes motions of gases in the translucent outer layers of stars, and the bias introduced by sinking rather than rising gases in the outer convective layers. It also examines (but dismisses) the possibility of the effect being caused by a non random distribution of velocities relative to the Sun due to some asymmetry in galactic rotation.

I'm not quite sure what they mean by how these velocity shifts relate to the use of cepheids as standard candles, in my day, the spectra were not an issue, and it was strictly the period-luminosity relationship which was considered for that purpose. Perhaps spectra are used for distance determination in some modern technique, or perhaps they play a role in calibrating the period-luminosity relation in the first place. It's been a while since I studied this stuff formally, and a lot of water has flowed under the bridge since. I certainly didn't want to plow too deeply into that article. However, I'm sure there is nothing about this related to non-cosmological redshifts, although I did note one of the researchers is from the Max Planck Institute, where Dr Arp works.