The idea is: suppose there is a universe that has elements that are fundamentally random. It is nondeterministic. Well, let that universe run for its lifetime, and record everything that happens. Then make a deterministic universe that just plays back the recording (this is the "second time around").
From the viewpoint of someone living inside the universe, there is no way to tell whether it is the first time around or the second time around.
...
But the other thing to point out is that this question presumes an old idea about the passage of time, which is that things happen in a sequence A, B, C, D, ... and that if you are at C then D "has not happened yet". But if you look at relativity, this appears to be a naïve viewpoint. In relativity, the time at a faraway point in space that you would consider "simultaneous" with your own clock depends on the relative speed between you and that point. As you speed up and slow down, you can make a faraway point "go forward or backward in time" with regard to which moment there you would consider "now". The crazy thing is that for angular movements the relative speed is amplified by distance, so when you are moving around at everyday speeds the "now" on planets across the galaxy is going back and forth by thousands or millions of years. (This is hard to observe because you are viewing tiny amounts of light from very very far away that have been traveling for a very long time, and the light that you are about to see was very close to you when you did the angular movement so it will not be much affected, etc, but hey, the math says what it says, you either believe what physics tells you or you don't.)
So when you make a distant "now" go forward, then backward, then forward again, do you expect the two forwards to be the same, or not?