Check the DirectX v9.0c and make certain it's on your computer as mentioned above. Even though you might have DirectX v12, you still need to install DirectX v9.0c - the one with the Steam install - so that the game can do the 3D properly. It will not overwrite the newer version, only add files. The newer versions of DirectX do not have all of the library files that SH4 needs.
Also, if you aren't getting the full "Properties" dialog, then you are either hitting the ico file, or you are in an incorrect folder and hitting the shortcut instead, or you're in the Steam Library, which also has a "Properties" dialog. You want this:
and go to this:
You might also have to tweak that "Change high DPI settings" dialog... That is for my SH3, of course, and with SH4, you can choose anything between XP and Win7.
