It is less linear though.
There's little to argue here : To reach the locked areas of DkS 1 you need to get to Anor Londo, the only way is Sen's Fortress, the only way to the Fortress is ringing two bells.
To reach the locked areas of DkS2 you need the king's ring, you can either grab 4 lords souls, including 4 times the same one sigh, or X brazillion souls. Then it's very much open, and although there's a linear sequence of things to do in order to reach the throne, you can reach the throne after bypassing most of the first half of the game. You can completely avoid the Bastille, the Mines, the Lava castle (forgot those silly names), these are big chunks of the game.
I felt like DkS2 was closer to Demon's Souls on some of these aspects (too bad it ended to be a fuckfest in terms of level design, boss design and so on). Including less mandatory levels.
I mean, there's linearity and linearity. Arguably, Demon's Souls is the most linear of the series, since the five worlds you get to visit are all designed as corridors, and the bosses are commonly referenced as 3-1, 3-2, 3-3 as there always is an unamovible sequence for each world. But it's although the less linear since you only need one Archdemon's soul to get to the end, hence there's no need to step a foot in the poisonous place or the tower of Latria if you don't like these. DkS2 is in that vein regarding this aspect. Well that's what I meant.