Apparently, Darksiders 2 takes place before / at the same time as the first game (during War's 100 year stasis between the Apocalypse and his return). So yeah, I guess it's fine to just play this... But then again, some characters are making an appearance (Vulgrim, Samael, perhaps Ulthane and, uh, that lady angel chick). You might just want to finish Darksiders 1 anyway just to be safe. After all, Death makes an appearance at the end of the first game...
Might as well play it. It'll take all of about 15 hours or less (depends on how much you know and how much you want to hunt for upgrades). I just ran through it this week to get refreshed on everything.
It's so rare that I complete any game now a day, but I beat the first one twice. Surprized you, even have to ask, as it's a great game. Constant different aspects where the gameplay changes significantly.
No one knows what it means, but it's provocative...gets the people GOING!!!
The only thing you need the first one for is to understand what Death is trying to do, otherwise its not really clear. In the first one, the Apocalypse is started early, so War goes down to Earth to see what's up. He is then blamed for starting it and has to stand trial before "The Council", who are in essence the 4 horsemen's superiors. The game begins right as War has to stand before the council.
In the game's lore there are Angels, Demons, and Humans. The Apocalypse killed off all humans, so Death believes that if he can resurrect mankind, then it will somehow spare his brother War from the council's wrath, as he would be "undoing" the consequence of beginning the Apocalypse. It really doesn't make any sense to me as there's another big reason why the Apocalypse screwed up the "balance", but saying it would be a spoiler from the first game.
As long as you know all the above, you're good to go for this game, as it doesn't ever really mention the first game ever again.