It looks like it is what is known as a 3-1/2 (three and a half) digit multimeter, which means that it can display 4 digits but the one on the left (the most significant digit) can be only a 0 or a 1, rather than any value from 0 to 9. So the maximum numeric reading it can display is 1999. That being one very tiny increment less than 2000, which explains why the scale choices all begin with 2. And the maximum possible indication with the 20K setting would be 19.99, corresponding to a resistance of approximately 19.99K (or approximately 19990 ohms). And, similarly, with the 200K setting the maximum possible indication would be 199.9, corresponding to a resistance of approximately 199.9K (or approximately 199990 ohms).
So as you can probably see the scale numbers are not multipliers. They are the maximum amount of resistance that can be measured on the particular scale, with the decimal point having to be adjusted by the user to get the approximate number of ohms. And as you can probably see the best resolution (and presumably the best accuracy) can be obtained by using the lowest scale number that is higher than the resistance being measured.
So it seems likely that the 6.77/6.75 and 2.19/2.18 and 8.97/8.95 numbers represent approximately 6.77K/6.75K ohms, 2.19K/2.18K ohms, and 8.97K/8.95K ohms respectively ("K" denoting thousands). Those numbers are all much less than the resistor values used in the Rothwells. That would work in the direction of making them an even better impedance match than the Rothwells with respect to the tube preamp, but a less good impedance match with the CDP. Although in this case that less good match would most likely still be good enough, given that the unspecified output impedance of this particular solid state CDP is most likely low. I would not drive those attenuators with many and probably most tube-based signal sources, though, as well as some lesser solid state components, because their higher and often frequency dependent output impedance would not do well when working into 8.97K/8.95K (and actually a bit less than that, due to the additional loading presented by the preamp or other destination component).
To be sure that the measurements are meaningful, though, and weren't taken on a scale that was lower than what was being measured, I'd suggest repeating the measurements on the 200K scale and verifying that the results are consistent. (Although I suspect that if the measurements were taken on a scale that was lower than what was being measured the meter would probably have given some sort of error or overload indication). On the 200K scale you'll probably see a reading of around 6.8 when measuring between the input and output center pins, corresponding to the 6.77/6.75 numbers on the 20K scale. And likewise for the other measurements.
Best regards,
-- Al