To be clear, the Gazelle article is the incorrect one - it advocates drying the phone first using a desiccant like silica gel or cat litter (though it says rice is the least effective of them). There is no mention of using alcohol (except in some comments).

The iFixit article advocates displacing the water using rubbing alcohol (i.e. open it up and dunk the motherboard/etc. in alcohol) - thus halting the corrosion that would continue if it were left to dry.

Is alcohol better than just patting it dry and blowing it out with some compressed air?

Yes. With alcohol you're displacing the water. With compressed air you might end up pushing it into new nooks and crannies it wouldn't otherwise have been able to reach.

But doesn't booze like to mix with water?

Yes, so strictly speaking you're not only displacing the water; you're dissolving it into the alcohol. But assuming you're using more than a tiny bit of alcohol, the water/alcohol ratio of the solution will be minuscule. Furthermore, if you pour alcohol over the components, the new alcohol will displace the just-formed solution.

It doesn't behave strictly that way. https://www.youtube.com/watch?v=PuV8ILW5cAQ