Yes, you need two interfaces. Remember the 15216 is strictly a pasive physical layer device. It's really only a precision packaging of some optical refraction and filtering to move light from one wavelength to another. It does NOTHING else. Any layer 2 or higher adjacency or connectivity needs to be established with your Catalyst interfaces.
That said, you only need to establish a ring if you are looking for ring-based protection scheme (e.g. POS). One could configure the three Catalysts in a "V" sort of configuration with one acting as the apex (and typically the STP root bridge). This would be less resilient than a ring-based configuration as that apex Catalyst would be a single point of failure. That is not necessarily a bad thing. I could imagine, for example, if that root Catalyst was in the facility with the data center, that connectiivty between the other two in and of itself would add no value in the absence of data center connectivity.
