The NEXT update adds multiplayer, and also a requirement for PS Plus and Xbox Live for the multiplayer.
There are a fair few games, even paid ones, that don’t ask for Xbox Live/PS Plus subscriptions for some, or all, multiplayer elements they include. For instance, Destiny on PS4 has some of its many locations and modes available even to non PS Plus subscribers. No Man’s Sky, however, will be joining the bulk of the games available on both systems in requiring PS Plus for the multiplayer functionality that has been added into it with the NEXT update.
No Man’s Sky originally did not need PS Plus on PS4, even though it did have some online elements, such as a shared universe (though full fledged multiplayer was one of the things that was famously missing from it at launch). The NEXT update, which will be available tomorrow on PS4 and PC (the Xbox One version, which launches tomorrow, comes with it beforehand) will obviously be changing that, however.
Of course, this makes sense and is totally fair- I don’t imagine there was anyone who was hoping that this game would let them play online for free, especially since that is almost never the case for non-F2P, non-subscription based games on either platform.