The configure script is not written correctly to detect the Slackware distribution. Currently it is testing for a file in /usr/lib/setup/slack*
This is non existent any longer (or never has been). What should be looked for is /etc/slackware-version. This has been standard on the Slackware distribution since 10.x when I started using Slackware back in 2004. Also, the default INIT_DIR for Slackware should be /etc/rc.d not /etc/rc.d/init.d. The init script should also be named rc.tmdns not tmdns.
I am actually working on integrating Zeroconf into Slackware. It would be awesome if we could clear these few things up. For now I have modified the configure script to correct these issues. If you would like me to upload it to this ticket, please let me know.