Squigs, your post reminds me of a good friend of mine whose father left at a similar sort of age - and when I say left, I mean moved to Oregon. He never saw his father again but as his father was the 'mixed race' part of him and was his spitting image (it was uncanny) he never quite got to forget him.
Anyway, a couple of years ago he got word that he'd died, teaching English in Korea. He'd never remarried or had any more kids so my friend was his next of kin. He had a hell of a lot of weird emotions about it all, because he'd had no meaningful relationship with his father, hated him for what he'd done to his mother, and for abandoning them all. But still he felt a weird grief when he died.
What we suppose is that he was feeling grief not really for the man himself, but for the father he never got to have. Grief that the last chance for him to be a proper Dad had passed, and now his father would always be the deadbeat he hated.
In short, don't be surprised if you get some weird-ass emotions (don't do the xkcd hyphen displacement thing with that...) over this. And as others have said, there is no 'correct' way to feel.