The following article contains spoilers from DC vs. Vampires: All-Out War #3, on sale now.
Nightwing's relationships with his former friends is complicated to say the least. While he is clearly hell-bent on establishing a new world order for his people, he also harbors lingering feelings for his surviving family. This is made even more obvious when it is revealed in DC vs. Vampires: All-Out War #3 (by Alex Paknadel, Matthew Rosenberg, Pasquale Qualano, Nicola Righi, Troy Peteri) that, despite having tried to assassinate him, Nightwing did not place a bounty on Damian's head.
This suggests that Nightwing does indeed still love his little brother, and most likely feels the same about his remaining family. Examples of this can be found in how he offered to turn Alfred. However, there is still a darkness and deviousness to him following his transformation. It's entirely possible that Nightwing might have spared Damian not out of love, but further plans for the young vampire.
When Batwoman offered to join Deathstroke and his team, he requested that Azrael, a former vampire, confirm if Batwoman truly is an enemy of the vampire kingdom. Azrael explained that there was a bounty on her head, but despite Damian having made the more egregious choice of attacking the king, he was strangely free of a price on his head. This little tidbit helps to explain why Damian has had so much agency in the world despite his actions; Nightwing never pursued him for revenge.
After Damian's botched assassination attempt, Nightwing did admit he wanted Damian out there in the world still. While he may have been trying to establish a kind of peace between vampires and humans, he suspected that Damian would have a part to play in this. Outwardly, he believed that Damian's natural compassion made him different from other vampires, tempering the worst parts of being undead with his own innate kindness. So, perhaps this is an extension of that. For Damian to live and thrive, Nightwing would have to let bygones be bygones.
Of course, there is another possibility. This is still the same man who deluded Batman for so long then literally stabbed him in the back. What Nightwing is thinking at any given moment in his undead state is anyone's guess. Perhaps there is a more sinister motive to letting Damian live. He admitted that there is a hierarchy, but that should Nightwing fall Damian would not be the heir apparent. However, he did not say that Damian wasn't in the line of succession.
It's possible that Nightwing is thinking long term. Maybe he does believe that what he's doing is necessary, but he also recognizes that humanity will never willingly submit to his rule. So, in the event they do find a way to kill him, it will likely decimate the vampire hierarchy. If Damian is safely on the other side and free to take over once the dust settles, perhaps that will usher in the peace that Nightwing wants, by trusting the Robin he helped raise.