https://www.cyclingweekly.com/news/h...as-queen-stage
This piece explained the potential gains.

A better way of understanding this choice though, is in terms of speed and cadence.

At a cadence of 100rpm, Roglič could ride at a minimum speed of 12.8kph on this setup. Compare this to a more common lowest gear setup of 39/32, which at the same 100rpm gives a minimum speed of 15.6kph. Faster, yes, but more taxing.

On a 18% gradient, a 70kg rider —even on a UCI weight limit matching 6.8kg bike— would need to put out a sustained 600 watts to keep up that cadence and average speed.

When on standard bikes, Roglic was pretty much the same as GT and Almeida on climbs, with GT having the edge if anything.
So I'd suggest there's good evidence to say the tactical change of tec won it for him.