I don’t know the precise answer, but I do know this:

1. Often the kind of measures that are about something vast and complex (like population for example) are really good approximations, not completely exact numbers. So maybe doesn’t matter because the number itself is not trying to be 100% accurate.
2. As far as I know those measures are made from the top down view, like with airplanes or satellites, so no it would not include inclines. To include inclines in a precise way it would have to be measured each one on the spot, which is not the way that is done. There are almost no field surveyors these days, again, as far as I know. And to include inclines in an approximate way takes us to point 1 again so it wouldn’t matter much if there were a small difference.
3. Why would we do that? Almost everything we use land for requires it to be horizontally flat, so we flatten it. For example, an irregular coastline doesn’t matter because we can use the crevices and irregularities to fit in more boats or ports or beaches, since the sea is horizontally flat and that is what really matter to us. But if there’s a hill with a greater area because of the steepness of it we cannot fit more houses or warehouses of streets. We have to flatten it first so we gain noting from it being inclined.

So form my point of view it would be almost as if we tried to include the sides of a ravine or gorge in the measure just because technically it is area space.

Sorry if I cannot give you an exact answer, but I wanted to comment because you raised an interesting point that made me think.

Cheers.