From my knowledge, you can either use the nuget CLI (which is just a portable exe you can download) and do nuget install Microsoft.GameInput to download and extract the package into the cwd, or download the package directly from https://www.nuget.org/packages/Microsoft.GameInput (.nupkg files are just zips). Inside should be everything you need, .libs and headers and such.

Well, it seems to that all I needed is to load the GameInput.dll, then I have the library to use, except I messed up the VTables, so I have to fix that first.