It’s possible that the DLLs it needs aren’t in the PATH. It will need the VTK DLLs, which are usually placed in site-packages/vtkmodules so that the VTK .pyd files can find them. The vtkRenderingTkXX.dll, however, won’t be able to find them there unless site-packages/vtkmodules is in the PATH.
Other than the VTK DLLs, I don’t think that vtkRenderingTkXX.dll needs anything except for the Tcl and Tk DLLs, and my understanding is that tkinter automatically sets the path for those, since they’re packaged with Python itself.
There are dependency trackers that can figure out which DLLs are missing, if you need one then I can check to see which tracker I’ve been using (my machine is at home, so I don’t have access to it right now).