I include Microsoft Word files (.doc) in my project, however when I double click one of them to open, NuSphere tries to open it on its own and gives me the error

How can I instruct NuSphere to let the shell open that file type?

Thanks!

Right click -> Shell -> Open With (or just Open)

I know I can do that, is there a way to tell PHPed to handle the file type properly?

"properly" is not a correct word in this situation. By requesting File->Open you tell IDE to open a text file in its editor. Nothing more and it does so.
Try .NET or another IDEs, they all do the same.
PhpED provides you an option to run it through shell.
Feel free to use it.

I guess I don't agree, if it doesn't know how to open the file and gives an error, why is it trying to open it?

NPI, but because you ask it to?
For all the editor "knows" you really want to look at the inside of that file... it is quite possible that you use the .doc extension for say PHP code or HTML...
I'm sure that if the editor would refuse to open the file because of an "unknown extension" a whole lot of other people would complain in here about that.
The Shell Menu > Open works perfectly as expected, as suggested above.

I guess what would make the most sense to me is that if the extension is not registered in "Associations" settings, then perhaps it should just let the Shell handle it automatically?

The thing that doesn't really make sense about the way that it works now is that it can't open the file, garbled or not, it just fails with an error.

Doesn't anyone else use word files to document their project? Doesn't anyone else run into this issue?