Spritz cipher sponge function capacity
The relationship between Spritz's security and the capacity of the internal function, Shuffle, is based on the fact that any generic attack must use on the order of $2^{c/2}$ queries to Shuffle in order to have a non-negligible success probability, where $c$ is Shuffle's capacity. A generic attack does not use any details about Shuffle, meaning the attack holds if you replace Shuffle with any other function. This does not say anything about attacks against Spritz in general, and if you're able to find a special property about Shuffle which is useful for an attack, such as a more efficient description of Shuffle, then you can beat the $2^{c/2}$ minimum requirement on the amount of Shuffle queries for a successful attack.

So the fact that Shuffle can be described more compactly will not change Rivest and Schuldt's security claim since their claim only depends on Shuffle's explicit capacity. In fact, Spritz's effective security could be significantly worse than what they claim, but you'll have to find an attack against Spritz to show this.