Let me add that you can obviously land in the park, as you have runways at both Furnace Creek and Stovepipe Wells. So another way of asking is simply: do you have to have an official runway to land? Obviously, you would need to stay >= 500 feet from people, but people don't typically wander too far from the parking lot and that's a big area. Staying away from people wouldn't be too difficult, especially in July or August when there's basically no one in Death Valley.
https://www.nps.gov/deva/learn/management/rules-and-regulations.htm says you would have to have special permission.
36 CFR §2.17 – AIRCRAFT and AIR DELIVERY
(a)(1) The use of aircraft on lands or waters within the park other than at locations designated by special regulations is prohibited. Death Valley’s special regulations at 36 CFR 7.26(e) authorizes the use of aircraft only at the following locations:
- Death Valley Airport, latitude N 36°27’50”, longitude W 116°52’50”, commonly known as the Furnace Creek Airport.
- Stovepipe Wells Airport, latitude N 36°36’15”, longitude W 117°09’30”.
- The Saline Valley Warm Springs Airfield, latitude N 36° 48.41”, longitude W 117° 46.90”, commonly known as the Chicken Strip, is open pending special regulation.
The landing of aircraft at locations other than those listed above, such as for wildlife research, is permitted only under conditions of a permit issued by the superintendent.
Aircraft have a significant potential for impacting park resources and human safety. By requiring permits for these activities, the superintendent can manage these activities and mitigate negative impacts.