Tou cant tell aperson wether or not their in love with someone if youre not them. Sure he dosent know about her life but that is not the criteria for loving a person
I'm pretty sure I can examine whether a fictional character is in love or not, and if the text says they are, if it's believable or not. And knowing about someone is a criteria for loving them. You can't love someone if you know next to nothing about them, have spent very little time together or have never opened up to each other. Their current relationship has all of this.
I think it's safe to say that he's developed a dependence on her. Maybe even has a crush on her. But love? Nah
Feelings are feelings regardless of where they come from, what the both of them need is to recognize and reconcile those feelings can satiate and help them form a better relationship
The Duke most definitely views FL as his saviour and understandably so, but he knows next to nothing about her independent life and her as a person so he's not in love with her. FL is there because of duty and it's no wonder she developed an attachment to the Duke's beast form and had those slight feelings (mothering, taking charge of) transferred over to the Duke himself. However, she doesn't know him and is under no obligation to get to know him so the Duke saying all of that to her is out of line and slightly toxic/manipulative as it's guilt tripping. HOWEVER, it is good that the Duke is self-aware and very realistic to show him struggling with this. I like this so far.