They’re usually done automatically by a program that includes people who have already input their family trees. Once everyone is in, then it’s just a matter of running an algorithm over the tree to pull out the relationship.
FamilyTreeMaker, which I use personally, does that for everyone I’ve put into the program. Because I use my tree for research, I have 25,000 individuals in it. So I frequently want to ask how two people are related.
But something like the WikiTree has IMMENSE numbers of people to run the algorithm on. That last box is encouraging people to run it for themselves to see if they’re related SOMEHOW to a Rothchild.
The problem is, if people aren't meticulous researchers (and most people aren't), their trees are going to have hundreds, if not thousands of people in them who aren't really their relatives, especially if they copy from other people's trees. The chances of something like that being accurate is slim to none.
One of the major complaints about trees on sites like Ancestry.com, FamilySearch.org, etc. is the inaccuracy of the trees that members have done.