Hard to say without actual evidence from controlled tests. I interpret the:
...may be gentler on your cassette and ring...
as it being softer metal and hence "gentler" on your parts, but this is sort of a fallacy, as others have pointed out in the comments.
It may be gentler, but will probably cause wear faster due to stretching and the pins not being "as hard" as the hardened chain.
So if you consider this "gentle" claim and weigh it with the fact that your cassette is probably getting "shark teeth" more quickly due to a (marginally) more stretched out chain, then yes, a softer chain could be considered gentler on the parts themselves, but I would expect the drivetrain as a whole to wear faster.
This begs the question; is it actually worth it to buy the more expensive chain?
If the extra wear (or lack thereof) of the cheaper chain causes me to have to buy 2 more chains and an extra cassette per season, than I'd probably go for the better chain. But if using the cheaper chain doesn't really affect my drivetrain consumables scheduled replacement (cassette, rings, chain, pulleys, lube), then I wouldn't be inclined to spring for the more expensive chain. Weight comes into play (i.e. hollow pin) but it is so minimal that I wouldn't really consider it unless I was counting grams. (256g vs 259g for Sram PC1170 vs PC1130 ).