While it would make sense that all they want is to be able to read your resume, and are asking for a Word document simply to avoid getting some weird formats sent in, you shouldn't assume anything.
For all you know they upload the Word file content into some database, or the person looking at your resume is only comfortable with Word. By not following directions you run the risk automatically disqualifying yourself for the position.
I would copy out the text part of your resume in a clean, simple Word format, and send in both the Word, and PDF versions. That way they will see how neat and tidy your PDF version is (if they bother opening it), and will appreciate the fact that you went through the trouble of creating a Word version.
What you provide them with also depends on how you submit your resume:
Some companies will have a form you fill out on their website, and a tool you upload your resume to. In this case I would not include the PDF at all, as uploading multiple files - some in the wrong format - might screw with the server side code. Instead, bring print-outs in person to the interview, and explain why you submitted an "uglier" version.
Other companies will simply list an HR email address, and ask you to attach your resume. In this situation attach both files (Word & PDF), and make it very clear why you are attaching both. Explain that the PDF version is meant to demonstrate mobile app design trends.
Just always make sure to give employers what they ask for.