I'd be thinking clamping, in particular at the back. The wall will keep it from tipping backward, you only need to take care of preventing tipping forward.
From the picture, it looks like there is a small overhang of the desk top on the sides. A small block on each side with a "lip" as deep as the overhang could serve. This could be screwed to the sides of the shelf unit if the unit was exactly the same width at the table top.
A unit with no shelf at the bottom would be nice because it would allow the desk surface to be unobstructed. You could put some strip lighting (like under-cabinet kitchen counter lighting) under the first shelf, which would provide good lighting without consuming desk surface. Depending on the height, you might need to place a "shade" strip in front of the lighting to prevent glare into the eyes of someone seated at the desk.
I expect you want the first shelf high enough to clear an open laptop.
Sturdy bent sheet metal might also serve as a clamp, and would be low-profile. All the screw holes would be in the shelving unit. Some rubber padding would prevent marring the underside of the desk top, perhaps something like an old inner-tube.