Why does mixing the salt and yeast sometimes work?

It doesn't work "sometimes", it works pretty much always. People are just being sloppy when they say "salt kills the yeast".

Certain levels of salt inhibit the yeast, so that it multiplies less, or slower. If you have an old or improperly stored package of yeast, or you are working with a strain which is not very resilient, then the negative effect may be enough that you don't get a healthy growth process established, and the dough doesn't rise at all. But it is a matter of probabilities, not of certainty.

So there is no reason for a recipe with a direct exposure of yeast to high salt concentration to not work, especially with today's modern, carefully engineered yeast supply. It just has a higher chance of failing when compared to recipes where the salt is added at a different step.

The recipe you linked is also not in any way critical. There you disperse both the dry yeast and the salt with the flour, and by the time you have added the wet ingredients and the yeast wakes up, the salt concentration is as low as it is ever going to be. The finicky recipes are the ones which ask you to bloom the yeast with a teaspoon of salt and teaspoon of sugar in a small amount of water, for example, or prescribe a different high-salt preferment method.

The vast majority of bread machine recipes add the salt and the yeast to the pan at the same time but not touching, then mix.

The recipes for mine all add salt (& sugar) to water, then flour, with yeast at the top. By the time the yeast gets wet, the water is uniformly salty.

What you do need to avoid (in general) is mixing dry salt and dry yeast, then getting them wet. Then you're trying to rehydrate the yeast with really very salty water. Even then, the overall effect is more likely to be a slowing down than killing all your yeast, but if you're working to time (or a machine is) that's a problem.

As mentioned a lot of the impact of salt depends on the concentration of salt.

To illustrate consider this graph

from this paper https://www.researchgate.net/figure/nfluence-of-salt-induced-osmotic-stress-0-10-NaCl-on-yeast-cell-growth-Saccharomyces_fig5_286917973

Its not great for seeing effects at the time periods we would be considering for rising but makes the point that increasing amounts of salt inhibit maximal growth. However, the amounts that have profound effects are at levels of salt that are unpalatable: most bread recipes end up around 1% final salt concentration; 5% would be incredibly salty when you consider that things like Vegemite and the like are about 3% salt concentration.