To call No Man's Sky a game in the traditional sense would be doing it a massive disservice. It's an experience, a simulated universe to live in that gives you freedom to do whatever you want to do in that universe whilst having a vague narrative about reaching the centre of the Universe.
So far I've put around 20 hours into the PC version, and in that time I've managed to warp to five different star systems (despite still being 170000+ light years from the centre) and mined and battled to my heart's content. In short, I've had a whole lot of fun whilst advancing the story very little.
Aesthetically, No Man's Sky is quite beautiful. The worlds you set foot on couldn't look more alien. Even the Earth-like ones have such a wild colour palette you couldn't mistake them for not being another planet. There's something about the technology aspect of the game that reminds me of Portal. Everything is sleek, crisp, and clean. I'm a huge fan of the look of the game. More often than not people follow the Star Wars design mantra of making a universe looked 'lived in', No Man's Sky does the complete opposite and goes for futuristic fresh tech. It's refreshing and I can see Hello Games' aim of making the game look like it belongs on the front cover of a 50s sci-fi novel has been achieved. You can find yourself spending a lot of time just admiring the vistas when you land on different worlds, or if you spot one of the procedurally generated lifeforms wandering around, chasing after those and trying to catalogue them. There is so much to do to pass the time in this game you could find yourself forever lost in it.
However, I can see how people would find this game a letdown. The lack of a constant narrative path may frustrate some. Some people need a clear story to follow. No Man's Sky does not provide this. It drops narrative beats, but what you choose to do with those is up to you. Communications with aliens is patchy at best. Unless you learn the lexicon of each species, you will always be second-guessing what they are saying to you. It adds a sense of wonder to the game that I really like.
The soundtrack is also fun, adding otherworldly vibes to the environment. It's not intrusive, but complements the mellow gameplay. It really is a marvel that Hello Games have achieved so much, with so few. That's not to say the procedurally-generated landscapes don't cause issues. You can find yourself lost in an underground cave with no apparent way of escape because it's not been designed by a human, little frustrating bits like that cause issues, but that's nothing to complain about, it's just another risk in the world.
The discovery elements of the game intrigue me. I still get a kick out of naming everything I see and uploading it, safe in the knowledge there's a slim chance someone else may stumble across my discoveries one day. There's a satisfaction to knowing that you're the first person ever seeing this place/animal/plant.
The mining and grinding aspect of the game is fun (if that's your thing). I spent hours stealing resources from a heavily-guarded planet simply because I couldn't resist. It was the equivalent of poaching, and I was soon upgrading my firepower so I could blast away any sentinels that got too curious.
There is so much you can do with this game. It's so vast, but for me it would never be a 'main' game. It's got legs on it, but I feel after twenty or so hours I've seen most of the tricks it has to offer that I thought were unique, but now they just look a bit like variations of the same thing. But I will continue to play. It has that ability to constantly draw me back in and the drive to see 'just one more planet' and to see what's over the horizon.
If you're a fan of survival games, or crafting games, then I think you'll enjoy No Man's Sky. If strong narrative is your bag, then maybe this isn't for you. It's a fantastic experience, but just an okay game. It can get quite repetitive and quite quickly. I like what it has to offer. I can see Hello Games expanding this game and adding new features over a long lifespan (there are already plans afoot for bases and freighters). This isn't the sort of game that will have a sequel, but it is the sort of game that deserves a long and fruitful life.