from what I can see in the dump everything looks fine. The browser asks for google.cz, MWG answers with 407 and provides possible authemtication schemes (NTLM, Basic). The browser asks for google.cz again setting up NTLM (NTLMSSP_NEGOTIATE message). MWG correctly sends a 407 with NTLMSSP_CHALLENGE message, then the browser does not continue. The browser now has to contact MWG again and send NTLMSSP_AUTH message in order to finish NTLM authentication, but the packet capture does not contain this request.
It could be a problem of browser/OS or an invalid response sent by MWG which I didn't notice. I recommend filing an SR with support to have this checked. From what I can see MWG works as expected.