Most word documents I open and select Save-As DOCX, I get the checkbox "do you want to preserve compatibility with older versions". But on a new document I'm working on, this isn't displayed. How can I change the setting on the document, and how can I check if the option is already set?
Older versions of Office do not support the .DOCX format, making the setting moot.
Try saving in .DOC format.
Microsoft Word DOCX documents come with two main compliances (there are more):
When you save a document with backward compatibility in Microsoft Word 2010 it will save as the Word 2007 compliance so both versions can open this document without any problems.
I can only guess that this document is already a Word 2007 DOCX document so this option is not needed. To be 100% sure of this can you attach the document somewhere so I can inspect?
I believe the easiest way to check this option would be to open the document in Microsoft Word 2010 and check for any messages notifying you that it's being opened in compatibility mode. I'm afraid I don't know of any other way through the UI.