DXR is platform agnostic really, AMD stated recently their full stack is already fully functional on the fallback layer, it's just only meant as a testing platform rather than for release products for the time being(There has to be application level support and implementation of the libraries for it to work), likely because their current stack wouldn't have much practical use for it in shipping realtime applications.
If Cryteks version is genuine realtime raytracing I'm sure we'll see their technique become a ubiquitous shortcut as part of DXR or implemented as a library alongside it as soon as it's documented and verified.
If Navi has improvements to the handling of certain operations, like FMA ops, integer ops & memory addressing amongst a few others, they could easily have a DXR layer that is somewhat useful.