full circle is 400 grad, so a right angle (10,000 km) is 100 grad.
Then minutes and seconds are factors of 100, so a centesimal minute is 1 km and 1 centesimal second is 10 m.
Etymology vs dictionary, I suppose.
How is it not? it's not a change to the actual distance (well, it is for a sufficient precision), but a change to the definition of the metre is exactly what it is. It's defined relative to the speed of light rather than a random platinum bar length, with the constant picked so that the actual measurement stay the same (up to a certain level of precision).