Tried it on a Garmin GPS III Pilot from N000 00.000 W090 00.000 to N000 00.000 E090 00.000. The GPS gives 10819 NM. This sounds about right as it would be 10800 NM if you assumed the world is a perfect sphere (It is not, it is slightly longer around the equator than from pole to pole) and the world is 21600 NM in circumference. (based on 360 degrees at 60 NM per degree) Straight through the earth would be 6875 NM.
So in answer to your question Huntsman it measures point to point distance at the surface as far as the GPS III is concerned.
Anybody else like to try the same experiment with another type of GPS ?
------------------
Push forward - Pigs get bigger
Pull back - Pigs get smaller
Pull back some more - Pigs get bigger again ??