There isn't even an attempt at justifying why high atmospheric pressure should be fatal to the Zetarians while allowing Lieutenant Romaine to survive. It's just a random thing that Kirk pulls out of his hat, in another demonstration that he can solve medical problems that his science officer and medical officer have no idea about.

The best thing about this episode is that Scotty actually gets a romantic plotline (without being accused of being a woman-hating murderer).

Transcript

1
Captain's log, Stardate 5725.3. Taking Lt. Mira Romaine to Memory Alpha to oversee transfer of library equipment.
Sulu: Captain! Some strange phenomenon!
Kirk: Yes, she fell for Scotty, not me!
2
Sulu: No, a space storm!
Kirk: That's actually less unusual than what I said.
3
Caption: The strange lights affect Lt. Romaine.
Scotty: Mira!!
4
Chekov: The storm is headed for Memory Alpha. It moves like... it is intelligent.
Uhura: Hailing frequencies, Captain?
Kirk: No, let's ignore that possibility for another 20 minutes.
5
Sulu: It's... attacking Memory Alpha!
Romaine: I see dead people!
6
Caption: Later, on Memory Alpha:
McCoy: Dead people. They're dead, Jim.
7
{back on the Enterprise}
Kirk: You saw it before it happened. Do you have any psychic ability?
Romaine: {possessed} No.
Kirk: Something's screwy here.
8
Sulu: The storm is back!
Scotty: Mira!!!
9
Romaine: {possessed} We are the last survivors of Zetar.
Spock: Life was wiped out there millennia ago.
Romaine: We survived. This woman will be our host.
10
Kirk: No! You can't have her. Bones, put her in a pressure chamber to kill the Zetarians.
McCoy: How do you know that will work?
Kirk: Captain's hunch!
11
Spock: You realise you are wiping out the last survivors of an ancient civilisation without offering them any chance to coexist peacefully?
Kirk: Shhh!
12
Romaine: Scotty, I feel much better.
Scotty: Now we have all the time in the world.
Caption: Exactly what James Bond said right after his wife was murdered.