I wonder if this can really be labeled as "romance".
First of all, there is the aspect that the machine runs on an A.I. that's part of an operation system that may or may not be designed by humans (or another computer program for efficiencies sake), making it impossible to simulate free will (yes, even in humans, free will is mostly simulated, and only a few human beings are ever able to make truly free decisions) as there is always a strict hierarchy in the program structure that cannot be breached, otherwise the whole device would become useless.
Then there's the issue with what romance actually entails. In most manga, romance is depicted as a mix of altruism and sexual attraction/affinity, completely devoid of any higher cause/strive.
We can rule out sexual attraction in case of this manga because "Mina" is not a human female, which would be required to fulfill the criteria of sexuality (you need both sexes involved to form a sexual relationship/for sexuality in general).
Altruism is also not really applicable because we have the relationship of owner and possession (not in the form of slave, because Mina is a slave to the company that produced her, seeing her being part of a cloud network; it's probably safe to assume that her operation system is also not hardwired but run by accessing a server cloud,which makes it easier for the manufacturer to maintain,control and update to prevent liabilities in cases of harm inflicted to property or life of the owners(s)).
Especially in case of an inanimated object like a robot, there is no genetic connection to trigger a genetic altruistic response by the subconscious mind, meaning what the relationship entails is mostly reduced to "philia" (love between friends/friendship) without a deeper connection to ones own identity (it would probably be possible to achieve that if the maincharacter was more aware of what it means to be human, but this is not some sci-fi story about humanity and transhumanism).
Last but not least, the key role in true romance, "agape" (or godly love) seems to be absent as well, as we don't see the main character involved in any religious practices, nor do we hear them talk about theology, which would be very interesting as a topic to explore on with the different outlook of artificial intelligence and human intelligence + human soul.
It would also be interesting to explore the topic if creation by humans is also indirectly divine creation, thus needs some sort of connection to the one that created their creator, thus in some shape or form creating a "familiar" bond with humans through the presence of a creator of the creator, being the "grandfather" in some shape or form.
Maybe this would enable the robot to "understand"/relate to some sense of altruism.
Without a god, there is nothing to marriage and no deeper meaning to a relationship between a man and a woman, making a couple just a pair of "strangers" working together for a common goal.
That's also the reason why only a man and a woman can marry, and not two other entities, even if politicians and ideologists want to convince people (who lack logical understanding and intelligence) otherwise.
Marriage is a pact between a man and a woman and their god(s), they swear an oath in gods presence to have him/her/them bear witness to their bond, and without religious involvement this cannot happen, and the "vow" just becomes another promise that is held down on paper by some government official and worth as much as any other promise you give to someone at your working place or to a stranger on the street.
With that said, it will be interesting to see what this story makes from the premise, but after reading Chobits I'm well aware that a story between a robot and a human does never involve romance, nor is a robot capable of actually loving someone.
However, it's actually interesting because it makes you question what love is, because even in humans, love is somewhat predetermined by many factors that we are unaware of (for example, genetic compatibility), thus not a choice of reason and free will, and it still takes determination and devotion to accomplish something you would call a fulfilled relationship as a man with your wife or as a woman with your husband.
In the end it comes down to what they can give, what they can receive and what they can achieve together, which is what Chobits built upon but failed to deliver as the story was cut short severely before anything could happen that would explore into this topic, the story basically ends on Hideki becoming aware of the fact that there are things humans and robots can do and cannot do.
I fear that this story might as well end on this premise and not having the main character going beyond that line to truly understand and adapt while being fully aware of the philosophical implications and consequences of his actions.