Sorry, I didn’t reply earlier and just saw this.
It works by using the Roblox friends API to pull each user’s friend list:
https://friends.roblox.com/v1/users/{id}/friends
Then, it runs a bidirectional breadth-first search:
Image Source: Discovering the Power of Bidirectional BFS: A More Efficient Pathfinding Algorithm | by Zachary Freeman | Medium
The source I linked explains it a little complex, so to simplify, it basically expands outward from both usernames at the same time until there is a collision between the two networks.
The reason we do this instead of searching in one direction is because it is faster to only have to go half the depth on each side.
The site rotates across a few proxies that mirror Roblox API so it is faster and rate limits are not as big as a hurdle, and there is a concurrency pool so that it scans multiple users in parallel at every layer. Because of this, the site will be able to return most paths in under two minutes even if there is 5-6 degrees of separation.