What is the difference between .doc and .docx?
.doc is the binary format Word used from 1997 to 2003; .docx, from Word 2007 on, is a zip of XML parts. They describe the same document property for property, which is why this viewer reads a .doc by writing out the .docx it stands for.
Why does Word say Compatibility Mode when it opens a .doc?
It lays the file out by Word 2003’s rules, which differ in small ways: justified lines keep their spaces, and an empty line can follow a page break. The PDF here follows the same rules, so its pages match what Word shows.
Can I turn the .doc into a .docx here?
No, the viewer never writes a Word file. Word saves one under File, Save As, with Word Document chosen as the type.