The thing for me is, Minecraft only gives you the most basic of tools to do stuff with. If you want a cannon, you have to do some pretty fancy planning and testing in order to get it, it's not a basic item you can just craft. In that regard, Minecraft is the better sandbox game for me, as it requires you to be very creative in there.
This game, on the other hand, seems to be putting a greater emphasis on the "lone survivor" aspect that Minecraft only gained later in development. There are superficial similarities here, of course, and I suspect that once the devs get around to polishing up the rough edges, it'll be an interesting take on the survival sandbox genre, but I cannot quite see it inspiring the same amount of insane creativity and experimentation that Minecraft got famous for. Remember that when MC debuted, there were no hints of the mechanisms and "story" introduced later. It was all about improvisation and creativity and playing in a sandbox; this game on the other hand debuted with both of its main modes already roughed out.