I just finished making a standing desk, the top board is 4x2 feet and is about 45 inches high. I am having a problem with the desk rocking back and forth. Here is a picture of it: As you can see at the bottom of the left leg there is a 2x4 (there is another one on the right side, that help stop some of the rocking, but not all it. And the bar going across the middle is there to help add weight on the bottom of the desk to help stop the rocking but nothing is completely stopping it.
If I see correctly, that your table legs are attached directly to the top with no apron at the top. That there is no rack bracing of any sort, short of the 1 1/2" by 3 1/2" faces and sides screwed together. The apron, when the legs are attached to it properly act as rack bracing to a great degree. Most table aprons are anywhere from 4 to 6" tall, although there is no hard and fast rule how tall it should be.
With a table that tall an 8" apron, properly attached would reduce wobble tremendously.
Moving it off the carpet would be a help too, since there is a 2X flat to the floor which does not allow the carpet to compress enough to give a solid setting. You could raise the bottom stretchers so the legs actually go to the floor, instead of on a 2X flat...
The primary trouble is that you've taken the tried and true four-leg table design and turned it into essentially a two-leg design. Add "feet" at the outermost points of the four corners to concentrate stability at the perimeter of the structure. Thread-in hardware is readily available, or simply screw on small blocks of wood at least 1" thick.
The second issue is your desk's proportions. You have a fairly tall structure with a fairly shallow depth. There's no getting around the leverage that this creates. All you can really do is add a bunch more weight as low as possible, or extend the lower frame outward toward the user.
Finally, thick, padded carpeting creates movement by being compressible. You could skirt that problem by using spiked feet like some loudspeakers of yore had, where they penetrated through the carpeting to solid subfloor, but that may not be practical.