Top-level domain (TLD) zone files contain at the very least name server records for all resolvable domain names. These zone files are publicly available for all generic TLDs (gTLDs) once requested from the corresponding registries.
These zone files were collected every day and the deltas between each day were computed to find when domains appeared and disappeared. In most cases, appearances and disappearances correspond to new registrations and expirations respectively. These deltas were indexed to create a searchable database of registration periods for each domain.
Zone files are not a perfect representation of registration status, but they are a useful starting point using pubalic data.