Strange that no one has mentioned extra credits yet. They did a whole 3 episode thing on this very topic:
https://www.youtube.com/watch?v=v8aiEsIW9IM
Short answer: No. Dark Souls is not a JRPG despite being made in Japan.
Long answer:
JRPGs focus primarily on telling a story with established characters. Final Fantasy, Breath of Fire, Secret of Mana/Evermore, Skies of Arcadia, Chrono Trigger, Fire Emblem, Legend of Dragoon, Wild Arms, Suikoden 2 ... they all have specific characters you know and love. They all have pretty strict story lines. You can also stop playing as the "main character" for a while to focus on side characters (if there even is a specific main character)
WRPGs focus primarily on making you, the player, into someone awesome, and letting you explore the crazy world as your awesome self. The Elder Scroll series, Fallout, Mass Effect, Dragon Age, Neverwinter Nights and yes, Dark Souls (2). Some are more story driven than others, but they ALL let you explore and customize your character and play. Does the Dovahkiin want to slay dragons? Or just collect cabbages? The Vault Dweller can be specialize in any weapon, pick any path and be anyone they want. etc etc.
Imagine trying to change a JRPG character: imagine if Chrono had the option of being female. Or you could make Ike a mage. On the flip side, imagine if a WRPG locked you down. Imagine if murdering a guard in Whiterun caused a game over. What if putting on that new Daedric Armor you crafted didn't actually change your appearance at all? Imagine Mass Effect with no dialog options. You talk to the person, scripted line plays, and you move on.
There has been some blurring of the lines recently, as each style tries to work in beneficial aspects of the other. But I think they'll always have that divide. JRPGs want to tell you a very specific story with a group of very specific characters who look and act very specific ways. WRPGs swap carefully crafted story for freedom. It's harder to have a tight plot when the character is free to do whatever they want. And it gets messy trying to keep a players options truly unfettered.