does the NFS * run with a Win10 PC purchasing via Steam?

@Alfreinter Yes, NFS Shift works on Windows 10. If you encounter an issue with slow loading, run the game in Windows Vista (Service Pack 2) compatibility mode. If you have an NVIDIA graphics card and have problems with the game (e.g. it immediately crashes), you might need to install PhysX System software.

• As you are aware, Steam still sells NFS Shift. This version works and is my recommendation to you.
• At least one reseller currently still sells codes for the Origin version. However, 1) while that reseller has been vetted by other sources (and you can find that reseller easily enough via IsThereAnyDeal.com), it is not on EA's "Trusted PC digital online retailers" shortlist, and 2) there is an issue with a couple of the DRM files on the Origin version of NFS Shift that requires replacing them with working copies from another applicable Origin EA game installation (which is probably why NFS Shift was removed from sale on Origin); this issue doesn't affect the Steam version.
• Alternatively, you could buy the game on DVD (e.g. eBay, Amazon) if you have a DVD or Blu-ray optical drive. Game patch 1.02: Europe; North America.