It’s never reasonable to close an airport to an airplane experiencing an emergency. It’s not something that’s done. At most, ATC might advise against it if something makes it outright dangerous to land there, but the decision ultimately rests with the pilot.
The airport wasn’t exactly closed. Due to weather conditions they simply couldn’t do visual approach. There was no ILS and GPS was jammed, so they had to be diverted. And after they were hit it was too dangerous to use any nearby airport in the mountain zone, even if the weather was fine (they checked Mahachkala and decided against it). Aktau was a really good choice.
Yeah, it was a good choice. Aktau is surrounded by hundreds of kilometers of a really flat half-desert. Had they been able to land at even remotely correct orientation, they could have landed almost anywhere in that general area and would have likely been fine.