Is the Story Mode Chronologically Linear?

I was playing through the story mode and I reached, and completed the mission in which:

Patrokolos challenges, and kills Pyrrha. Pyrrha was the 'new Nightmare' having defeated him in a previous mission, defending Patrokolos.

However, the storyline then immediately cut to missions in which:

Z.W.E.I. approaches, challenges, and defeats Graf Dumas/Nightmare.

After those missions, the storyline jumps again to:

Patrokolos challenging Pyrrha again?

What the hell is going on here?

I believe the answer to your question is here. If you start reading the faq at episode 16 of the story mode, the author goes through the events of the last few fights of the game. A quick breakdown:

Episode 16 - Ivy unlocks the true strength of Soul Calibur. Patroklos vows to save Pyrrha and protect the world by destroying Soul Edge, but he stabs and kills her instead amidst a battle where she is opening a gate to Astral Chaos. He freaks out, gets stuck in Astral Chaos, and wants to go back in time to change his actions, which seems to be facilitated by some old dude also in Astral Chaos.

Episode 17 - You flash back to Ivy unlocking the strength of Soul Calibur, but this time, when it's handed to Patroklos, he sees what happened at the end of Episode 16. The old dude in Astral Chaos tells him to "fill the sword with his will, and wield the sword, not be wielded by the sword." Patroklos does and leaves Astral Chaos.

Episode 18 - (Note that Pyrrha left with Tira at the end of Episode 11) The short version: This happens prior to Episode 16 and shows Pyrrha killing Z.W.E.I. before Patroklos showed up. Tira gives her Soul Edge and Pyrrha opens Astral Chaos, the same purple gate you saw in Episdoe 16.

Episode 19 - This is Patroklos' return from Astral Chaos after seeing that he killed Pyrrha the first time. He wants to change that and his stint in AStral Chaos allowed him to do it. Think of this basically as time travel by Patroklos to correct a mistake. This time in the fight, he doesn't kill Pyrrha but instead gets Soul Edge away from her.

This is why this fight happens twice. From Astral Chaos, Patroklos is able to go back and not kill Pyrrha like he did the first time. This might as well be a DeLorean or TARDIS instead of Astral Chaos, since the effect is the same.

The remaining story is just as non-sensical, and involves Patroklos realizing that Sophitia isn't actually Sophitia but the spirit of Soul Calibur, which wants to control Patroklos.

Edit:

To actually answer the question, the storyline is linear for Patroklos. THe rest of the cast does not experience the first fight where Pyrrha dies because Patroklos goes back in time to change that event.