You wrote that "But there is no warping restraint required in this calculation example (it is Case 3 in AISC Design Guideline Series 9)."
Here is my opinion on that.
Case 3 on page 58 of the AISC Design Guide stands for the following torsional end restraints :
At left support : Theta = 0, Theta' (first derivative of Theta) = 0
At right support : Theta' (first derivative of Theta) = 0
In the table on page 108 of the AISC Design Guide 9,
Theta = 0 stands for no rotation,
Theta' (first derivative of Theta) = 0 stands for cross section cannot warp
In other words, case 3 represents a condition where neither end of the member is allowed to warp, which means, warping is restrained at both ends. In this situation, as shown in equation 2.3 on page 3 of the Design Guide, the twist at any point along the longitudinal axis of the member comprises of a component which is associated with the St.Venant's Torsional Constant (J, or IX as it is known in STAAD) and another component associated with Cw, the warping constant.
So, in my view, the AISC Guide does assume that warping restraint is available for case 3.
As I wrote in my previous response, in STAAD, the default condition is that both ends of a member are allowed to warp freely. For this case, the twist in the member is solely a function of the St.venant's Torsional Constant J. That is why STAAD is not using Cw.
To ensure that STAAD uses Cw, you need to specify SET WARP.