Yes, if you want to be precise about it, and for at least two reasons.
The GPS satellite clock will actually appear to run faster (on average) for all observers (and faster at every time for both itself an observer standing on the Earth, but possibly sometimes slower for an observer in free fall down a deep well). I know you referred to “kinematical” time dilation but that isn’t really a separate thing as the separation of effects into “kinematical” and “gravitational” is only an approximation to the full GR effect.
But it’s still wrong if we just define the “kinematical” part of the approximate split as the effect that would be seen if the satellite was not in orbit but just moving at constant speed in a straight line. In this case it is true that what was the satellite clock now appears from Earth to be slow; but it also appears to the (ex)satellite observer that it is running faster than the Earth clock. And unless we specify a way to decide who’s impression is right then it is wrong to say that either clock actually is running slower.