If “A function maps every input to a unique output, where as a relation can map an input to multiple different outputs”, wouldn’t a binary relation have the same problem? I know they mean to say a binary relation isn’t a relation in that sense, but that text could do with better terminology.
Also, and more importantly, I don’t see how “binary” is essential here. What is essential is the uniqueness constraint. Compare Relational Algebra (https://en.wikipedia.org/wiki/Relational_algebra) with SQL.