All things DNA is full of code that doesn't get activated and is just passed on anyways

Gene expression is what they mean by "activated"

Basically think of it like having a library of instruction books and only grabbing a few of them to do the project that needs done.

DNA contains coding and control regions. Changes to the coding regions are rare, most of the evolutionary stuff is happening within those control regions instead. Mutations there are more likely to result in interesting effects by affecting the way genes activate and interact, while the coding regions do the heavy lifting.

Losing some feature could be as simple as a mutation that permanently switches off the control region of a gene, even if the gene itself and the interactions formerly coded around it still work. Over time, those accumulate mutations and degrade, since they are not useful and therefore evolution doesn't preserve them, but they are still there. For example, we have an inactivated gene that used to make an enzyme that would break down uric acid. So we get gout, but our ancestors didn't.

I recall that scientists reactivated chicken genes for teeth and grew a toothed chook

I agree, this seems pretty misleading. And are there any other feathered animals other than on the dinosaur branch? Because if not, how should the feather DNA even end up in mammalian DNA?? Or maybe feathers are produced by very common differently used genes? But in this case this would be even more nonsensical...