Kirk took the test three times, if the first time through it was a surprise, not there after. Even if the tester changed the scenario each time, Kirk knew what to expect.
That is the point! If it was a test to "experience fear in the face of certain death", you would not be able to take it three times. Ever played scary maze 3 times and still get surprised?
It was a test of CHARACTER. No matter what you do, you lose the simulation. You simply cannot win, because every time you might save the ship, they add another bunch of problems. Most cadets would simply live with this fact and move on. Kirk didn't. AND he found the solution to the no-win-scenario. Which is why he got the commendation for original thinking. He did not cheat. He probably did what Starfleet was always looking for.
His son, who wanted to kill him an hour before, sarcastically said "He cheated." But he didn't take the test and didn't know anything about it.
And then there is this little dialogue in TWOK:
KIRK: You're bothered by your performance on the Kobayashi Maru.
SAAVIK: I failed to resolve the situation.
KIRK: There is no correct resolution. It's a test of character.
SAAVIK: May I ask how you dealt with the test?
KIRK: You may ask.
In the TWOK novel there is a scene right after the simulation. Kirk in a briefing of the cadets. And he gives Saavik yet another scenario to think about. She's on a sinking boat with another person, the water is full of sharks, what does she do? When she answers she would sacrifice herself, he provokes her by saying that the other person isn't worth the money Starfleet invested into her training or something like that. Then Saavik gets angry, and he learns something about her.
That is the whole purpose of the test.
They got it right in TNG, too. When Wesley had this surprise test at the academy in which he had to quickly decide who to help. And when Troi took the command test and had to send someone to death to save the ship. Test of character. You can't save everyone and have to sacrifice skilled people and even friends, which is also a form of the no-win-scenario.
And in the new movie, the new purpose of "experience fear in face of certain death" doesn't even make sense. NOBODY in the simulator room was afraid of anything. Uhura and McCoy were both annoyed, but not afraid. The bridge set had a huge set of panorama windows with observers looking down on them, the effects and graphics were not convincing at all. That is totally not how you invoke fear.