The RTX 2080 realtime ray tracing hype

Is it something that only nvidia cards will be able to take advantage of?
NVIDIA just being the first to make a dedicated GPU for ray tracing with its RT core, the others can follow suit as DirectX DXR (and Vulkan later) is an API that takes advantage the RT core. Basically NVIDIA just introduced a new GPU family model.

Will we have to make separate project that falls back on “baked” lighting or the old methods for AMD users and the stardard way of doing things for them?
Note that this whole ray tracing thing is an alternate rendering method than what we usually have in real-time graphics. The one we usually have is called rasterization. So ray tracing only complements or adds more choice on the rendering method (and you can switch between these methods as you like runtime, supposedly due to this nature). To answer your question, I don’t think there there is any changes required for your project unless you want to fully optimize your work only for ray tracing.

What happens when you have a large open world and want to make even more things using the ray tracing like the global illumination. Is it still possible to use all of the ray tracing effects in a situation like that?
The idea of the RTX is it has a dedicated RT core, which means you could say most of the rendering (the crazy rays going around for lighting determinations to create shadow) is done by that core + the tensor cores utilizing AI deep learning to perform NVIDIA’s denoiser to reduce noise faster. So there should be no difference (or even, better) than what we have now. It basically transfers the load from the normal GPU cores to the RT core, maybe leaving the main core to deal with only the shaders and whatever I dunno.

One more thing. Basically I’m in a dilemma because I’ve already got a 1080ti but not sure if it’s going to be worth it since the ray tracing seems to be an Nvidia only feature. Does the DirectX ray tracing API somehow make this all cross compatible once an AMD solution is released?
Ray tracing itself is not new, and DirectX provide the DXR API as GPU agnostic I believe. The function is to simply target to the RT cores, that’s all. It’s pretty much like shaders, specifically compute shaders. The one that people should think about is the denoiser algorithm which is made by NVIDIA, but even that I think is provided as gameworks (software), which I think should work with other GPU as well.

Hope this helps.