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They were specifically interested in the question of whether there were enough of them in the world for this to realistically occur, so their model did take this into account even if it didn't simulate every tick of the world directly. (and the answer is yes: on the seed they found there are enough pumpkins and snow blocks for this to eventually happen).

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Including the random walk from where the snow golem happened to get put and the one open portal in the world? That doesn't seem likely at all to me.

That's pretty much what they describe in the video. The random walk itself is not simulated tick-by-tick, but turned into an faster-to-compute model of the longer term statistical behavior of the walk. It's not quite a case of 'it would happen in the real engine at exactly these points with this seed', but more a statistical argument that it would be expected to happen on that kind of timescale.

But he's assuming that sometimes snow golems causes a creeper to target them, so these are random walks on a minefield, very finite.

Sure, but it doesn't need to be infinite, just large enough.

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