If you can access the attic area above the closet, you can easily determine if the framing is BEARING. If the framing runs parallel to the ceiling joists, the wall is not bearing, it is called a partition wall.
I see a typical double top plate framing and a third stud (new) to fram out the closet opening. Makes me think this is just a built-out closet.
If the framing runs perpendicular to the joists, it might be bearing. You will often see a header or a larger structure to support the upper weight. You will also see doubled 2x4s on the ends, sometimes 4x4 and a 2x4 to carry the weight down to the foundation. In your pciture, I see single stud framing attached to the double top plate, again suggesting this is a partition wall.
Oh, and if your single story house is built with trusses in the attic, the interior walls typically will not be load bearing either. That geometry carries the weight to the outside walls.
Can't wait to see what your attic search shows you!