ftfyquality chances and quality shots aren't completely different, but they are very important, as you stated.
And as far as the kings are concerned, they are not only outshooting their opponents on a regular basis, they are also outchancing them. Here's how the scoring chances break down for each game (at even strength):
+4 against ana
even against nash
+6 against van
-5 against phx
+5 against edm
+2 against col
can't seem to find the chi game, but let's assume that was in the minus column.
Source: robert_p. - posts - @robertjftc
i think this was mentioned already, but they also have no players with a negative corsi rating.
Once the goaltending stabilizes and they finish their chances, the kings should start piling up points no problem.
Right now, we're dealing with an awfully small sample size of games, and unfortunately it's a short season, so waiting for things to stabilize can be problematic. But for the time being, i wouldn't be too concerned.