genomics - How many dinosaur genes are in a chicken genome?

I read recently that we can "work back" to a dinosaur by selectively turning off certain genes in chickens, and we were able to create a chicken with a snout instead of a beak.

How many dinosaur genes are still hanging around in a chicken genome? I understand there is a lot of overlap for vertebrates, but shouldn't these genes have shuffled out over time?

Otherwise, couldn't we work back to worm or even earlier life forms? Is the whole history of a creature's evolution contained in its genome?

Edit This was a news story about a month ago. Here's excerpts from the BBC's write-up: "Chicken grows face of dinosaur: A chicken embryo with a dinosaur-like snout instead of a beak has been developed by scientists"

To understand how one changed into another, a team has been tampering with the molecular processes that make up a beak in chickens.

By doing so, they have managed to create a chicken embryo with a dinosaur-like snout and palate, similar to that of small feathered dinosaurs like Velociraptor. The results are published in the journal Evolution.

Link to Evolution paper included.

Also this piece from about a year ago: "Paleontologist Jack Horner is hard at work trying to turn a chicken into a dinosaur"

In 2009, the world’s most famous paleontologist made a bold claim. In “How to Build a Dinosaur,” Jack Horner proposed re-creating a small dinosaur by reactivating ancient DNA found in its descendants, chickens.

The toothy snout is already here. At his lab at Harvard Medical School, Matthew Harris has made chicken embryos that express ancient genes for the growth of conical, crocodile-like teeth.

Answer

Be careful when reading media as they tend to exaggerate. That Abzhanov paper is interesting; it will be better when it's published and the figures released. He does a lot of evo-devo work surrounding beak development. What they did in this paper was to inhibit in chick embryos two signalling pathways (which are actually conserved amongst all animals, not just birds and reptiles) so that their expression domain more closely matched that of extant reptiles (which lack medial activation, as opposed birds). They found that doing so results in premaxillary and palatine bones which resemble ancestral archosaurs. While incredibly interesting, this is a far cry from creating living chickens with dinosaur snouts.

To somewhat answer your question, chickens do not contain all of the genes that dinosaurs once had. They will have both gained and lost information. There will be much conservation in the same way that there is conservation between all organisms. For example, the Wnt pathway studied in this paper is conserved across all animals, from chickens to humans to placazoans to, presumably, dinosaurs. It's impossible to say how much has changed since we do not have any whole dinosaur genomes, but it's also important to note that it's not only which genes an organism has but also when and where they are expressed and how they interact.