This stretch is nearly impossible to see whether it's working as you do it because of the position in which you must stand. If you are not able to tell if you are moving the horse, have a friend watch from a few steps back.
How to do the belly lift
Press along the horse's belly on the centerline. There are several pressure points that work, but the easiest one is at the girth.
The horse will raise his barrel and flatten out his topline.
Note that although the Butt Tuck also raises the barrel, each move stretches a unique part of the horse's musculature and thus both are beneficial in their own ways.
If you are able, work with a trained equine body worker (such as a chiropractor, masseuse, etc) familiar with horse yoga to make sure you are doing this safely and effectively. There are also many videos online to walk you through the process.