Relationships
The defining characteristic of hierarchical dimensions is absent from the Schedule dimension: the parent and child relationships. The result is that the Schedule dimension does not contain hierarchies. Relationships are used within the dimension, but they are limited to memberships.
Even in this, the Schedule dimension differs from hierarchical dimensions in an important way. Unlike hierarchical members (which can join only one group), schedule lines can join more than one schedule.
In a true hierarchical dimension, the equivalent Schedule dimension's structure data requirements would not satisfy the minimum requirements to define the hierarchical dimension because the Schedule dimension does not have parent relationships.