Quote from the MSDN:
Compressed GZipStream objects written to a file with an extension of .gz can be decompressed using many common compression tools
GZip files are not really "zip" files. They usually use "gz" as file extension. You might try that, maybe Gmail is very strict about "matching" extensions and compression formats.
If you are using .NET 4.5 you can alternatively use the ZipArchive class. That one actually handles "zip" files.