Is there any way to print an OOXML document (.docx file) without having MS Word installed?
It works nicely via the MS Word interface but I need to find a way to use
Well yes and no. Yes it is possible without MSWord but you will need an application or library that understands ooxml. There are many other products now that do support (as pointed out by Devin) but if your requirements says you cannot have any of them on the server then...use a library and do it yourself.
It will then depend on what platform you are developing in...for instance there is a OOXML4J library for Java. And there are other libraries for other platforms as you will find here.