As an (admittedly amateur) student of Trademark law and parody law, this was a fascinating case.
And it largely comes down to how this dog toy was marketed. Which is to say, the Supreme Court is not giving it a pass because the dog toy is selling itself wholly as a product meant to look like the trademark holder's product.
So, the thing to keep in mind here based on my reading of the actual decision and my understanding of the trademark law protections: The SC wouldn't have sided on the side of Jack Daniels, had this "Bad Spaniels" dog toy been in a colorful box of other novelty toys. Because in that hypothetical case, its "identifying trademark" would have been the box/branding that the toy was found in, rather than the bottle shape and label design.
Even though I couldn't find a "Bad Spaniels" trademark filed with the USPTO, the Supreme Court is granting that its identifying trademark IS the bottle shape and label design, because there is no other branding involved and no other that VIP (the dog toy company) can possibly claim.
With Wacky Packages, this is simply not the case. There are many layers of diffusion involved before a Wacky might face a similar issue.
But where this case COULD affect Wacky's might be in the physical product novelty space. So, a 3-dimentional parody sold individually in the shape and form of the trademarked product, COULD face similar issues. At least a trademark case wouldn't be summarily dismissed.
But things like t-shirts, Wacky Packages themselves, and so on, seem quite safe, even in the wake of this decision.
Had this dog toy been packaged in a neon green box with an inset photo of the dog toy, it may well have found itself insulated from this complaint. But as it only offered up what it was, with its only trademarks being those that mimicked or parodied those of Jack Daniels, the court decided that JD had a legit trademark dispute.