They look close, but Omi Gibson is someone who wouldn't be that carefree about her cosplay.
The vid shows Raiden in a more loose fitting military-esque looking trench of a darker color. Along with this, his usual body suit/machine parts can be seen easily. In Omi Gibson's attempt, she's simply wearing brown slacks and black dress shoes with a tan colored trench.
I'm pretty sure it was one of the unlockable disguises + Raiden's mask/hair? I think that's his hair, cuz Snake doesn't have layered white like that. idk.