I'm not completely sure, but from what I understand DLSS is based on training a neural network by Nvidia on their premises, which is then only used for interpolation on the graphic card. It's the only way that makes sense.If it were trained locally, that would require a lot of resources and, at first, the results would be bad.
FWIW, you can build, train and deploy neural networks on the CPU, too, not only on GPU's. I'm pretty sure it could be done on AMD GPU's, Im unsure what would be the performance hit.
In the case of Nvidia, I think the approach was inverse, they had some AI capabilities sitting on the die (due to the pro-market requirements) and they tried to find a nice way to use them for gaming. What is unclear to me is what is the cost for Nvidia for training a NN for each game. I'm guessing it's pretty big, otherwise they would've done more games by now. The advantage, however, is that there is no hit on the graphical part of the card. I have a hard time seeing how AMD could come with a better solution, or a decent solution, not involving AI.