You’re right, the other person does not have to reciprocate.
But, the OP didn’t say that the cute coworker was going to cheat on his girlfriend. She only said that another female coworker thinks he’s fair game because there’s no ring on his finger. And the OP was asking if the absence of a ring is a strong enough hindrance…as it indicates a commitment.
It’s not about reciprocity here…more about the ring and it’s symbol of being taken.