Apple isn't trying to prevent Super Healthy Kids from using that logo. It's opposing their applied for federal registration of trademark.
Super Healthy Kids may already have trademark rights relating to that logo. You can have such rights without having a federal trademark registration - either through state registrations or just through you having used a given mark. Further, you can use a given mark even if you aren't entitled to (or haven't effectively acquired) trademark rights relating to it. Regardless of whether Apple is successful in this opposition, Super Healthy Kids will be able to use that logo. (I think there's almost no chance Apple could, even if it tried, win an action trying to stop Super Healthy Kids from using that logo - at least based on any trademarks which Apple has which I'm aware of). Further, Super Healthy Kids may still have trademark rights associated with that logo and be able to stop others from using it or something very close to it.
All that's at issue here is Super Healthy Kids ability to federally register a trademark. Such registration would give Super Healthy Kids some meaningful advantages - e.g., presumptive ownership and national rights, even if it hasn't (or doesn't) used (use) the mark nationally. It's asking for an enhanced ability to prevent others from using the mark (or something very close); it isn't asking for the right to use the mark itself.
When someone asks for federal registration, that request is (at some point) published for opposition. It's kind of like... if anyone knows any reason why this mark shouldn't be federally registered, speak now or forever hold your peace. That's not quite true, people can still challenge the trademark (or defend themselves against a trademark action) later - even if the mark is federally registered. But it becomes more difficult to do so once the mark is registered. The registrant is presumed to own the rights to that mark, even if you were previously using something very close. You have to overcome that legal presumption that they own the rights to that mark. So the time to challenge, if you have concerns about a to-be-registered trademark, is when it is published for opposition.
Since Super Healthy Kids is asking for federal registration of the mark in areas which overlap Apple's use of its own marks, Apple is opposing that registration because, among other reasons, it believes that mark could dilute its own. I don't think this case is a lock for Apple and I don't think it's a lock for Super Healthy Kids. I think the dilution question (rather than a likelihood of confusion question) is close enough that it could go either way, though I think it's more likely to go against Apple. It's possible that Super Healthy Kids just agrees to tweak its mark a little and Apple agrees to drop its opposition. (Apple has been successful that way in at least a couple of instances - with Woolworth's and with NYC).
But, at any rate, Super Healthy Kids' ability to continue using that mark isn't at issue. It will be able to regardless.