The statement "a OR b" is logically equivalent to "NOT a → b". They mean the same thing in boolean logic. If you walk into NOT a in the graph (meaning a is false), you are forced to walk into b (meaning b must be true). That is exactly what OR requires.
The reverse edge handles the symmetric case. Together they capture the constraint perfectly. This conversion is the foundation of the entire -SAT algorithm. It turns logic into graph structure.