How can TSP be an NP-optimization problem, when a feasible solution $s$ must be polynomial bounded in the instance size $|I|$?
A solution in the TSP problem is a sequence of $n$ vertices. 
Consider a labeling $1,\dots, n$ of the $n$ vertices. 
We need $O(\log{n})$ bits to encode the label of each vertex. 
Then, any sequence of $n$ vertices can be described by $O(n\log{n})$ bits; the concatenation of $n$ vertex labels. 
Hence, any solution $s$ of the TSP can be described by a number of bits that is polynomial in $n$. 

The size of the instance $I$ is also polynomial in the number of vertices $n$, as noted in the original question.