It's been a while since I read the paper in detail, but, IIRC, it _is_ using normal graph walking algorithms. They're just implemented in SQL.
That it's implemented on top of a relational database seems like a red herring to me. The relational model just defines operations on sets of tuples. A graph is just a particular kind of thing you can construct with sets and tuples.
From there, the query planner and execution engine take over, and an incumbent RDBMS's query planner and execution engine are supported by decades and decades worth of accumulated dark knowledge on how to optimize execution plans and efficiently traverse large datasets in the presence of a hierarchical memory model.
By contrast, Neo4j (to take an example) has a steeper hill to climb. Both in terms of not having had to spend decades trying to compete with Oracle, and in terms of being implemented in a less-than-ideal language for chasing raw performance.