After saving the stream to disk and doing a binary comparison to a proper docx, I figured out that it was in fact wrapped in a Compound Document File: http://www.openoffice.org/sc/compdocfileformat.pdf. I googled the first few bytes
D0 CF 11 E0 A1 B1 1A E1
which is the identifier of the CDF format.
The package can be extracted from the Compound file using OpenMCDF.