It's not that Google is trying to outsmart its own search engine, but verifying something that SEOs already know. Paid links still work. Google has not mastered sniffing them out yet. That all assumes that Google is paying for these links in hopes for SEO benefit.
While I completely agree with you, the one thing I question about the restaurant tv example is, does the child zone into the tv because it is something they rarely experience and provides changing imagery that catches their eye?
Again, I don't disagree with the overall point, I just wonder if their interest that you are experiencing is due to the intrigue of something new and not necessary zoning out just because it is a tv.
Is the NYT the new paid search police? I love that someone is targeting these black hat tactics but it is interesting that the NYT keeps publishing articles with sites and sending findings to google. I guess if it keeps putting google and the buyers in the media it will help with the ultimate goal.
Your call to action needs to stand out more by using a color that will pop. It currently blends into the rest of the page. Instead of "Register Now" it should say something like "Start Tracking Your Goals".
In your case I would do a couple of searches on Youtube for video and Google images/Flickr and compare the number of results that they report. That should give you a high level idea on the amount of content out there for your topics.
"Almost half of the top 100-selling iPhone apps are for preschool or elementary-aged kids"
I have a 15 month old and he loves watching us play colorful games or apps and his attentiveness has amused me, especially because he has no interest in TV.