Nope, perpendicular to the geodetic latitude
Indeed it is according to your reference, which I've now looked up. But my question arises from the fact that, in a gyrocompassing Inertial Navigation System, the "down" channel is aligned with the local vertical[1], and the corresponding velocity equations provide a "basic description of the Earth relative velocity evolution in a
local level navigation frame"[2] (my emphasis).
A GNSS-derived velocity, on the other hand, will be expressed directly in an Earth-centered Earth-fixed (ECEF) reference frame[3], as long as the standard broadcast or precise ephemerides are used[4] (admittedly I've never heard of an application where a non-standard ephemeris was being used, perhaps referenced to a different system or using non-Keplerian elements, although in theory that would be entirely possible).
Note however, that as long as navigation is taking place in a different reference frame (typically ECEF, for any long range terrestrial navigation) then presumably every relevant output will be transformed to the target system. This, I assume, will be the case in a modern craft with INS-derived velocities before they are presented to the user, which would validate Kayton's definition.
Now, the difference in geoid-referenced to ellipsoid-referenced groundspeed is negligible for all but the most demanding applications. To put this in perspective with a practical example, consider that an aircraft travelling at 400kt G/S will cover 2000nm in 5 hours. Let's assume that said ground speed was referenced to the "wrong" vertical and that the vehicle travelled over relatively rugged terrain resulting in an average vertical deflection in the direction of travel of 20 arc-seconds over the entire distance covered. The corrected groundspeed in this case would be 400*sin(20"), giving an ETA difference in our example of 2000/400 - 2000/[400*sin(20")] = 5*10^-4, or about 1.8 seconds, which is likely well below the measurement precision of most systems.
An interesting discussion, nevertheless.
[1] M. Grewal et al. "Global Positioning Systems, Inertial Navigation, and Integration", 2nd ed., Wiley Interscience, New Jersey, 2007, p31.
[2] R. Rogers, "Applied Mathematics in Integrated Navigation Systems", 3rd ed., AIAA, Blacksburg VA, 2007, p105.
[3] Grewal, p92-93
[4] A. Leick, "GPS Satellite Surveying", 2nd ed., Wiley Interscience, 1995, p487.