How does "SIPING" increase fuel mileage? - as some claim

Two things. First, aftermarket re engineering a tire is pretty much a compromise of intended benefits. Like, who would like having a summer tire with improved ice traction that were now louder then heck the other 9 months out if the year; gas mileage asside.

Secondly, what makes you think advertising is always true. They probably sell nitrogen too. They are after people who want something for nothing and are too cheap to buy dedicated winter vs summer tires. Generally, gas mileage is secondary to improving the traction on a tire designed for safe winter driving.
They’re just throwing dung against the wall and hoping something sticks in the eye of the gullible buyer.