DMOZ (The Open Directory Project) was once one of the most prominent and comprehensive human-edited directories on the web. The DMOZ listing checker tool you mentioned, available on SEO Check Points, allows users to determine if a domain is listed in the DMOZ directory.
Although DMOZ officially shut down in 2017, some tools and legacy copies of the directory still exist, and the DMOZ listing checker tool may be using one of these to provide its results.