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If the 2x4's that run horizontally are setting in notches in the vertical 2x4's, and not just screwed onto them, then they are fine. The bottom horizontal members look to be sitting in notches which works. The top ones, appear like they might be as well, though the paint (or missing paint) is throwing me off.
 

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With that sagulator site you linked, the thickness of the shelf ends up being the height of the 2x4's (3.5") the plywood on top if any, adds to that measurement and adds lateral stability. with roughly 600 lbs on each shelf, the deflection is 0.02" total (without any plywood).
 
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