It's kind of a way to retroactively back the game if you missed out on the campaign. After the Mighty No.9 debacle, I swore to never help fund another game in my life, and naturally I missed out on these backer exclusive items. What you get with this is simply that, access to these items for around the same amount of what I assume is a standard kickstarter pledge of 10 bucks.
Fair warning, if you are planning to buy this to have a cool sword from the beginning of the game, THIS IS NOT WAT THIS DLC PROVIDES.
What you actually get with this is an additional quest that you can get from Lindsay, the old woman that hangs around the main hub between the two descending stairs that lead into Dominique's/Anne's and Johannes' rooms; the quest can only be completed after you've succesfully defeated one of the final bosses in the game. The task you are given is to fight and defeat the creator of the game itself, who will now appear as a boss in the late stages of the game. The Sword Whip is intended as a weapon you'll get to use as part of the 'end game content', so to speak.
*Spoilers ahead*
To find IGA, after defeating Gebel with the Zangetsuto to the get the good or bad ending instead of the, uhm... weird one, all you have to do is reenter the boss area where Gebel was and he should show up for a fight.
*Spoilers over*
Once you've defeated IGA, go back to Lindsay in the main hub to claim your reward.
So, how does the sword perform? Pretty good I'd say. It isn't the best in the game by any means, but it can be handy in a backup slot for dealing with enemies that tend to move around out of range a lot. It has a decent damage output too. A quick tap of the attack button will make it do a short, non-extended attack, while holding the attack button will make it do an extended whip-like attack.
If you want an extra weapon and boss fight and don't mind the 10 dollar price tag, then you should get it; otherwise, you don't really miss out on much.
