Are you actually mapping the styles?
Yes, they are being mapped when they are imported in to InDesign
Have you tried saving as .doc or .docx -- whichever on eit currently isn't -- or .rtf in Word and importing that?
I have created Paragraph Styles, and they match the Word Document, but when I import the word document it ignores the font/style and directly imports the chinese font used within Word.
Our entire workflow is built around placing translator's Word docs into InDesign. In my experience, you can either struggle with this at length and maybe never succeed, or you can simply get used to clearing overrides after placing styled Word text.
If you for some reason can't just place, select all, and clear overrides, then there are many possible issues you can chase after:
Style naming - do any of your styles in ID have the same names as built-in styles in Word?
Style inheritance - are any of your styles in either app based on other styles? This can cause overrides quite easily
Character styles - are there any applied?
Font naming conventions:
I had a feeling that InDesign was not recognising the font used within Word, hence it was unable to change it.
This happens to me all the time when using fonts with localized font names. Also when paragraph styles in Word have bold or italics applied to fonts that have no bold or italic faces (i.e. Chinese fonts in Word will often get fake bolds or italics applied).
That is just a brief sampling of the difficulties inherent in placing multilingual text in Word/RTF into InDesign. Word import is simply troublesome in ID - my solution is simply to map a keyboard shortcut to Clear Overrides, and to use some scripting to clean up imported Word files.