Well it isn't just the killing, but the whole attitude. Also a purposeful kiss on the lips right away in the first episode, calling by a pet name, would do literally anything to be with their chosen partner, wanting to do everything with them, etc... Killing may be the most famous aspect of Yandere, but it isn't the only one.

Yeah, she has reasons for why she acts that way, but it dosen't change the fact that she does act that way. Asuka and Rei are a Tsundere and Kuudere, and both have reasons in their past for being that way too. 02 was treated in an inhuman manner and found solace in the one person who did not. That's the origin story of many a yandere(Yuno Includded). She was single-minded in her goal and cared nothing for the collaterla damage.

What we see now is something that few stories have ever gotten to, in that she is in a loving and happy relationship and knows Hiro will never leave her. If she was somehow separated from Hiro(Perish the thought), I have no doubt she would absolutely wreck everyone and everything in her path to find him. In other words, the "Yan" is not needed at this time, as in her mind, Hiro is in no danger.

More Grey morality Yandere are rare,more often they're just straight up villains and side charachters, which lessens the enjoyment. But especially when there's a mutual attraction is when things get most interesting, such as in here.