In many cases, studs that are sitting directly on the subfloor are not structural. Perhaps the only exception, and this would be only in homes built before 1955, before the building codes were introduced. If there is a joist directly under the stud bottoms, they may be bearing.
The main concern for wall removal would be to be certain to maintain a good connection/support at the base of the stairs. In my opinion, this should be no problem, since to add cupboards all the way to the lowest end of the stairs would seem impractical. Keeping the 1 short stud there will do all needs to be done for anchoring/support, should it need it to begin with. Another thing to look at is the stringer that the studs connect to. If there is the equivalent of a 2X6 left over after the notches are cut to set the treads on, there is enough "meat" there to handle the span that is left over from my suggestions.
The last thing to look at is the connection at the top. if you take out 3 studs, leaving the last one intact at the top of the stairs, it may offer you a 4' wide area for a cupboard. Depending what the studs do beyond the camera, you may be able to get over a 5' set of cupboards.
These suggestions are the simplest way to accommodate what you ask. There are framing anchors that can be used at the top to aid in removing even more studs potentially, but that would require more info on what you have.
