The only purpose I can think Ryu to wield this weapon like a Nunchaku though swinging it with a different style. Ryu can also use this weapon to deflect projectile attacks.
If you think about it, the Vigoorian Flails and the Nunchaku are exactly the same however the difference between them is that Vigoorian has a blade at both handles and allows Ryu to wield it in a devastating way (to `slash` of-course). While a normal nuchaku is designed to knock out opponents.
Now the Manriki-gusari can be considered the third type of a Nunchaku and the moves Vigoorian Flails couldn't do, the manriki-gusari could do.
The weapon can work like Ninja Blade's Twin Swords.
Forward to 1:42
As for Ninja Blade's Twin Sword, I'm not sure what it is, I can't really tell by the animation. Though I can guess they are Flexible Swords, that weapon is my favourite, regardless of it being the weakest:)
But please watch the video and look how Ken Ogawa uses the Twin Swords, now imgine if Ryu could wield the Manriki-gusari similar to it? Ryu would wield the Manriki-gusari like the Vigoorian Flails but with more advance and fluid moves, and also the manriki-gusari can deflect projectiles once swung like Ken Ogawa's Twin Blade.
Please watch this video , the author doesn't want to display the embed code:/
It's a demonstration of how the Manrikigusari can be used and swung.