He's claiming that there is no Doppler effect here?
Not when you find objects with high red-shifts that are apparently within our own Galaxy
High red shift within our own galaxy means high velocity. The only reason higher and higher red shifts was associated with greater and greater distance was because it equated to an early expansion phase of the universe.
Two objects 100k light years distant, one receding at twice the rate of the second must produce different red shifted frequencies.
High velocity is the key. One potentially valid criticism of Arp's observations may be that what he is seeing is the artifacting effect of Galactic Lensing of far distant Quasars being magnified to appear closer than they are. I find this very questionable in that they are now claiming that EVERY one of Arp's observed objects is such a Lensed Quasar. . . now over 100 of them. What are the odds of that occurring? That a quasar exists with a lensing galaxy placed just exactly right to make it appear closer than it is? Possible? Maybe. Likely? If so, Quasars must be very populous on the fringes of the Universe.