For example, we have dinosaur bones, but very little actual dodo fossils (apparently only one foot and one piece of jaw [1]). The way this project is described, they will not need DNA of the dodo itself, only of its closest living relative (Nicobar pigeon) and closest extinct relative where we have DNA (Rodrigues solitaire). The genome of the dodo will be recreated by interpolation.
Could that work for dinosaurs? Why not? There are lots of living relatives (all the birds, including the famous Cassowary, which some call a "living dinosaur"). We can do lots of genome interpolation, and we can identify the genes related to various morphological features. Not different at all from what they plan to do with the dodo.
Would we ever get actual dinosaur DNA? Never say never. But even if we don't, it's quite likely we'll be able to deextinct the dinosaurs, if we can deextinct the Dodo.