What the page says was called the classic case of dog-whistling is a whole advertising campaign.

I checked what Goodin's book (cited at that point in the Wikipedia article) actually says. It doesn't reference any specific advertisements in the campaign, and in particular doesn't describe the specific one you picked out as dog-whistling. It does, however, say this:

The fact that the practice is noticed, that it has acquired a name and a bad press, suggests that the message is not literally inaudible to others beyond its intended target. They have noticed it. And by identifying the trick and giving it a name, they have (after a fashion) worked out a way around it.

all of which seems to be in line with what I've been saying.

[EDITED to fix a spelling and add: I don't have a copy of Goodin's book; I checked it using Amazon's "look inside" feature. This means that while I was able to look up the bit quoted in Wikipedia and the bit I quoted above, I couldn't see the whole chapter. I did, however, search for "not racist" (two key words from the specific advertisement you mentioned) and get no hits, which I think genuinely means they don't appear -- it searches the whole book even though it will only show you a small fraction.]