You can't authenticate with an alternative kerberos implementation in the ThinLinc client on Windows. Only Microsoft's built in implementation works.
See bug 5816 for Heimdal Kerberos authentication.
The use case is that you in some cases want to use Kerberos authentication against a ThinLinc system that has absolutely nothing to do with the Active Directory domain that your local Windows machine is a part of.
Under Linux you would just do "kinit user@OTHER.REALM", but Windows lacks any such tools. So people install alternative Kerberos implementations for this.
For reference there also floats around a bunch of different patches to add support for this for Putty, so there is some precedence for supporting this model.
For reference, Firefox supports using GSSAPI instead of SSPI on Windows. Relevant settings are: