Yes, they can. Airports are heavily regulated by the Govt (FAA, TSA, OSHA, DHS to name a few). If one of these agencies determines that an airport can't 'operate safely' (vague term) they can order it closed until 'conditions improve'.
Below is purely my speculation:
I assume they'll say that there's not enough of <insert job type> to operate safely. I'm also anticipating them creating that shortage by voluntary or involuntary detail of employees to a larger airport to cover staff shortages there.
Some (not all) of the airports on the list have larger airports in the geographical 'detail area'. As a rule involuntary details have to be within a 'reasonable' commute for the employee involved. When I was still working that was considered within 50 miles, but you got per diem if it was more than that. So if you worked at, say, Fresno/Yosemite and had the choice between being laid off without pay or taking a detail with per diem to, say, San Fran or Sacramento (both 100+), which would you choose?