In truth the LubeGard PSF shown doesn't state that it 'meets' any spec. Like most multivehicle products, it uses "suitable for" to describe it's use. Doesn't mean not a good/quality PSF, in fact being a synthetic PSF and Lubegard, likely a quality product. Not sure about the cost though.
Doing just a little googling it seems PSFIII equivalent to Dexron II/III ATF. 'If' true an easy spec to meet with ATF, including the Multivehicle Synthetic ATFs like MaxLife. My advice, google Kia PSF III equivalents, and go to some of the Hyun/Kia vehicle specific forums and see what the folks are using. Most I see using a Dex III 'or better' ATF equivalent, some MultiVehicle ATF products. And the LubeGard 'suitable for' listings would 'seem' to confirm information. Power steering systems are nothing more than a simple hydraulic system. Nothing Special. You could use any ISO 32 or 46 hydraulic fluid in that system without a problem. A pump, a reservoir, hoses and a cylinder. Sometimes a cooler.
Thank you. I did some searching and found this to be the case. Not 100% sure I feel confident about using ATF in a PS system, but I guess that's what the KIA fluid "was" at some point. Not much on the KIA forums regarding this question. Most have advised as you have.