He wasn't that young (25) but had a fiancée 5 years his senior (30)... and that age difference showed. And they most likely had only been dating for 6 months or so? So, that might also play into the way they presented themselves.
It's not an actual age thing, though emotions probably play into it — but he probably would have looked 12 with a fiancee his own age, too. He had a very young-looking face at the time (pretty much that 'softness’ Felix had) and he hasn’t for several years, and I’m sure the heavy nicotine played a part.
Edit: I know this thread is meant to be pictures, but I couldn’t find where this excerpt from their engagement should go:
LA: The Danish press has put some emphasis on the age difference: the woman being older than the man. Does that mean anything to you, Miss Alexandra?
A: Prince Joachim very kindly translated to me in the newspapers today what he had time to do, and the papers had very, very kindly said that they didn't think that the age difference was a big problem because Prince Joachim matured very early and he's a very mature and sensible person and I tend to very much agree with that!
TK: Apart from being a wife, will you continue with your own business career?
A: I think it's very important to have your own interests, be it hobbies, business, work, and I'm very much an independent person. I'd very much like to keep doing something of my own, yes.
TK: What kind of things?
A: To be honest with you, I cannot answer that until I've actually lived there for a bit and seen what opportunities there are.
LA: Prince Joachim, will you allow the Miss Alexandra to have a room with computers so she can trade on Hong Kong walls?
J: Well, seeing as I haven't, well, I have a very, very, very faint idea of what that part of business is like, whereas Alexandra has a hell of a lot more to say in that, if she feels confident in trading long-distance, that's perfect with me.
TK: Miss Alexandra, do you expect to manage your husband's estate?
A: I'd very much like to be involved in it... [video cuts]
It does seem to line up. Joachim has always been pretty serious, or at least broody, even with that earlier smiley face. Also Alex knows a lot more about the Internet and business than him. Still holds up.