They have said literally the entire time that it isn't multiplayer. The closest it gets to being multiplayer is that you can upload your discovery's to a database so other's can see them.
No Man's Sky's Website wrote:
Choose whether to share your discoveries with other players. They’re exploring the same vast universe in parallel; perhaps you’ll make your mark on their worlds as well as your own.
In parallel, not simultaneous. It's the same universe, but you're in your own instance of it, not a shared one.
The steam store page also only says single-player, not multiplayer.
Wartheft
