I have heard that also, but Mazda does have non-boosted shortened compression cycle engines that they still call "Miller cycle." All their current boosted Pseudo Miller cycle products use turbos and not superchargers. Unlike the 1990's Millenia engine which uses an IHI supercharger. All various car brands' modern Atkinson engines are Pseudo-Atkinson cycle anyway, as they all use variable valve timing to achieve the shortening of the compression cycle.
The non-boosted Mazda Miller/Atkinson have all the benefits that the boosted ones do BTW. Personally I would tend towards buying the normally aspirated cars for reliability and simplicity reasons. They seem to have 2L minimum on engine size, at least in the US market, so no worries about 1.5L lackluster performance with these. If you go back and look at the MPG figures in that switchover era in 2013-2015 for Mazda, its readily apparent the fuel efficiency benefits of their switch to the Atkinson engines. For one example their model "3" 2.5L gets 37mpg highway EPA.
Did not mean to belittle the Geely achievement, but the shallow Atkinson engines have been out on the world's roads for twelve years and seem extremely reliable. They pass Euro, Asia, and US emissions standards. In twelve years if this deep Atkinson tech proves to run as reliably and cleanly, at that point it will prove itself to me. I feel the same about the compression ignition gasoline engines. Or "Homogeneous charge compression ignition." An interesting idea, but so far an unproven track record.
Sorry for the Mazda nerd rant.