I haven't seen or heard from you in 5 years. But I still google your name and ship to see where you are and if you are still in the Navy. Even though I'm married and I don't love you anymore, I still hope you are happy and wish you the best.
No, I would say that that is just being concerned about a past love. I still care about my exes and I've moved on from them. It's not like the writer is stalking them or anything. At least it doesn't seem as such from the entry.
I wouldn't agree that she/he hasn't move on or that she/he's obsessed. It's possible to care about someone that you once loved without being obsessed or needing therapy.
Sometimes I do this with a certain boyfriend from high school. I definitely have no interest in being with the person ever again. It' okay to be concerned or care to see where they end up in life.
I do the same thing. He was my first love, but I have no interest in being with him again. I was happy to find out he was making something of himself. The way he was then and for awhile after we broke up, I was afraid he was going to end up dead or ODing.
I think it's perfectly normal to worry and care about past lover's wellbeing.
When I go searching for my first love, I always hope that he is doing something for himself and he's not. He is the same type of person he was back in high school. I hope one of these days he wakes up and realizes what he has been doing with his life.