We've got a rather complex "can of worms" here. Some of the quoted material seems to confuse cause with effect, or to confuse static effects with dynamic effects.
Shouldn't the restoring (yawing) moment resulting from a sideslip be bigger when the aerodynamic damping is less effective?
It seems like you are imagining that with less damping acting in opposition to yaw rotation, the restoring moment from sideslip will somehow be able to act more quickly or more effectively to introduce a yaw rotation to end the sideslip.
That's not a correct way to view the situation.
To understand why, you have to realize that the root cause of aerodynamic damping of yaw rotation is that the yaw rotation automatically creates a difference in sideslip angle between nose and tail. The whole fuselage can't all be experiencing zero sideslip. If the tail (vertical fin) "weathervanes" into alignment with the local airflow, the nose will be experiencing a sideways flow that generates a yaw torque that opposes the yaw rotation. Similarly, if the rudder is used to keep the nose aligned with the local airflow, the vertical fin will be experiencing a sideways flow that generates a yaw torque that opposes the yaw rotation. And note that the steeper the positive slope of the curve shown in the textbook, the stronger this opposing yaw torque will be.
At high altitude and high TAS the aerodynamic damping on the rudder is less effective, so directional stability decreases shown by a reduced positive slope.
That's not really a correct way to view the situation either. A reduction in directional stability ("reduced positive slope") really can't be explained as a result of "damping". A reduction in directional stability ("reduced positive slope") could be the result of effects related to high Mach, but it's not completely clear that this is in fact what the quoted text is trying to describe.
The truth is that whenever we talk about "damping", we need to specify exactly what mean to say is being "damped". Generally we are talking about a dynamic effect--something related to the rate of something else. So is the quoted passage trying to address aerodynamic damping of the rotation rate in yaw, pitch, or roll? Or is it trying to address damping of an oscillation, such as the pitch phugoid, or such as the "Dutch roll" oscillation? Or are we actually talking about a reduction in the "weathervane" yaw torque per degree of sideslip (i.e. the static directional stability) for a given IAS-- which would not be a conventional usage of the term "damping"? The quoted passage fails to clarify this.
It's true that some oscillation tendencies tend to be most pronounced at high altitude, for a given CAS or IAS, but the quoted passage hasn't adequately explained why this should be so.
Increased static directional stability would be expected to cause increased damping of yaw rotation rate. It's confusing to suggest that increased damping of yaw rotation rate causes increased static directional stability, and decreased damping of yaw rotation rate causes decreased static directional stability, as the quoted passage seems to do.
There are at least two different reasons why an aircraft tends to be more prone to various dynamic oscillations at high altitude (and therefore high TAS), for a given IAS--
One, strong damping of yaw or pitch rotations tends to reduce "Dutch roll" or pitch "phugoid" oscillations, respectively. And for a given IAS and G-load, a higher TAS will be associated with a larger radius (smaller rate) of curvature of the flight path, so the stabilizing effect of yaw or pitch damping will play less of a role in the aircraft's dynamics.
And two, at high Mach numbers the slope of the static directional (yaw) stability curve is indeed reduced.