See, I don't think Ness' home sickness is all that mechanically different from Steve's hunger. It's just a glorified (unseen) resource bar you have to manage. Yes, it colors his character ever so slightly, but not by much.
Also, Minecraft gives you objectives like the Achievement List (which is more directly connected to Minecraft than in most games) and there are things to do like kill the Ender Dragon that are not directly communicated to you as the player, but serves as one of the "goals for your world." Like, the entirety of the original Dragon Quest is just going to kill one Dragon too. Along the way you have to get better gear so that you'll actually survive that fight. The only real difference is there's an extremely minor amount of characterization you get along the way.
I don't see why the freedom a game offers suddenly makes it less narrative-ly less deserving. Yes, there is no official language of communication in the game other than through grunts, but is that experience really defined differently or any less valid than sweeping narratives. If you subscribe to the ideas of the medium is the message (you're free to claim Minecraft has no message, just as I'm free to claim it does have one about creativity and exploration,etc.), then there's a little bit more to Minecraft and video games in general that you can really dig into. I think there's a super compelling point to be made of games that use gameplay to tell their world and story are more compelling than those that lean on the trappings of other artistic mediums (text dumps are famous in old video games and how many modern games resort to long cut scenes that are glorified animated movies). Yes, it's a randomly generated world that has very few limits and that you're free to operate in as you see fit, but there's still an experience for the player to be had and goals that you can choose to partake in. All game goals are optional at the end of the day too. Like, yes, developers assume you will participate in their curated content... but then you have people deciding to act out their lives as NPCs in Skyrim despite how much "true content" there is to be experienced. I just don't think there's all that much that separates Minecraft and other titles with self-inserts, and that such a difference isn't really important in the long run.