If it was just generic "come sign up for our new dating service!" messages, I'd agree with you, but that's not what they were doing.
If it were to become more common (not sure how common it is actually...probably very), that could result in an overall poor experience for OKCupid users who would associate using the service with receiving spam that never netted out to anything.
There is nothing wrong with OKCupid drawing the line on another service trying to get "free" marketing on its dime and at the expense of its user experience.
That said, if it never amounted to anything -- as in, I got Dating Ring spam promising dates that never materialized, I would be pretty pissed.
However my point was that it is not exclusively Dating Ring doing this. It is important to consider the overall signal to noise ratio when you factor in the messages from Dating Ring and any other company out there trying to use OKCupid's platform to promote themselves.
OkCupid, barring the creation of a program/partnership specific to this case, has decided that overall, it is worth filtering out. If they thought it added value based on the data they had, they would try to partner with Dating Ring. Heck, it would likely have been fine if Dating Ring purchased ad inventory on their site. As it stands, it seems they view this approach as spam per the OP. If it is against their terms, Dating Ring doesn't have much leg to stand on as that would make it a pretty black and white situation.
Part of me wonders if a Cease & Desist is en route to Dating Ring's office.
Such situations are exactly the kind where Kant's categorical imperative applies. If something is clearly wrong when everyone does it, it should not be OK for a particular company to do.
Just off the top of my head. And then consider that, by the context, they probably meant anyone who hasn't had a new message in a while. Yeah.
TL;DR: Lots of good reasons.