Blame the French for reinventing the wheel instead of, say, using a 1/1000th of a nautical mile as the definition of the metre. Alas, that's all water under the bridge by now.
If you want to do navigation in SI units, the UTM projections (see sibling thread) typically do positioning in metres inside each grid square.
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).