The fact that it need an internet connection alone can´t be the reason for not being able to pause the game, right?
Yeah I don't think so (see the next part however for my thoughts on the full reasoning why there is no pause) - D3 also was always online (sans console editions) and you could pause with a few exceptions.
There must be some real time interaction going on between your “world” and the worlds of others.
There definitely is a shared world state component, in that you seamlessly matchmake with others who can appear near you, and engage alongside you - this also grants you some extra XP ("Nearby Player Bonus") while someone else is close. It becomes even more apparent during world events, such as world boss fights or Legion Events (which you can think of as a mini world boss fight).
I think this is where the true cost of not being able to pause comes from - since they didn't add in a private vs public mode (in D3, you couldn't pause when you had the game set to public, or when friends were in your game). If it existed, and you were to pause as it is, you'd need some sort of immunity buff or such, as another player could cause enemies to come near you, and either kill you outright, or right when you resume the game.
Hm, I read up on it for a second and it seems like there is a portal that you can use to teleport to a safe place? A town? Supposedly you can even do that from within a dungeon AND even teleport back to the same place?
Yep - this is nice to have (though you cannot use it in a boss fight AFAIK) though it'd really be nice to be able to actually pause still, but I suppose it's better than nothing.