Without knowing the specifics: renting land from the feds inside a national park is not entirely the same as renting land from a private person in a commercial zone.

From a park-management perspective services offered inside a national park close when the park closes. The park-restaurant doesn't get to reopen that park or its services any more than the hotdog vendors force Wrigley Field to open on the weekdays...

Just like a mall closing for safety reasons: even though there is a buck to be made there are also liabilities and requirements. If the park isn't offering its rangers/personnel/management/responsibility then they don't want to be simultaneously advertising to the public that they're open for food sales. They're not open, they're closed.

My guess is politics. If you want voters to push to end the shutdown, make it hurt regardless if the shutdown requires it.

This also happened with national parks. They actually chained up the entrances during the shutdown as if people can't access a park if the gov't is shutdown.