If I remember correctly, that site was actually used to publish an early paper about fingerprinting. Their database is simply people who visit their site. You probably are unique among people who have visited! I doubt it sees much traffic anymore. This would explain the parent being unique also now that I think of it.

There are a few studies that used sites like that and got lots of traffic (by advertising on sites like HN) from non-normal users.

There was a landmark study done in France that measured fingerprints through a government website. The general population was much less unique.

Edit: found the AmIUnique paper: https://scholar.google.com/scholar_lookup?journal=Proceeding...