In any case, this has nothing to do with client certificate as the returned ERROR_WINHTTP_CLIENT_AUTH_CERT_NEEDED error in the code seems to suggest.
That may be true for Gears 5 but the winhttp tests show that renegotiate can also be initiated because the server wants to authenticate the client. ERROR_WINHTTP_CLIENT_AUTH_CERT_NEEDED should be returned to the app in that case to allow it to supply a certificate.
I believe in other cases renegotiate should be handled transparently like in your patches, but it's not clear to me how to distinguish them. Note that this is also discussed in bug https://bugs.winehq.org/show_bug.cgi?id=55105