Thibaud, The straighten and level tools I referred to are on the Edit menu of the Panorama Editor:

The straighten option is also available via the icon in the task bar, as in your video. I was just alerting you to the two features, which do different things. The straighten option simply uses image parameters and ignores the content of the individual images. The level option uses vertical and horizontal line control points which you must have created yourself on suitable vertical and horizontal features. As in your video, you can level or straighten the panorama manually. To assist in this process, you can drag to the right the tiny triangle in the middle of the bottom edge of the Panorama Editor frame to overlay a grid of variable size. When you run the optimizer, the level panorama function will by default be run automatically as a final step. However, you can instead choose to allow the optimizer to make use of the horizontal and vertical line control points in the main optimization by selecting the option "Include in single pass" on the Advanced page of the Optimizer tab. In this mode, take care to give the images freedom to move about as needed by checking appropriate y,p,r paramters. (Unchecking y,p,r for an anchor image would prevent the levelling of the entire panorama).
John