My understanding is that because the knee travels a good bit more forward during the shrimp, this makes it challenge the quads more (knee dominant). The pistol, thanks to having an entire leg to counterbalance you in front, allows you to "sit back" a lot more, so I think it would be a bit more hip dominant. This is only when you compare one to the other.
This is of course relative since the pistol resembles a front squat more than a back squat, so in the grand context of things, the pistol is usually thought of as more knee dominant.
Also, just for everyone's knowledge. The airborne lunge is as explained in TNW, with reaching forward with one or both arms. The shrimp squat is specifically the airborne variation where you only reach forward with one hand. The jumbo shrimp squat is done on an elevation. Just some unnecessary nomenclature hehe.