The weight will be applying pressure to where the anchor/screw would have to shear off. Shear strength of a screw is the strongest.
Take 24" wide cabinets 36 in high made of 3/4" plywood, 3/4" shelves and loaded with dishes. You would probably have the same weight as he is talking about spread over the same distance.
The key is get the screws far enough into the studs so that it is solidly mounted. Use at least 4 screws and it should be fine. If you can get 4 on top and 4 on the bottom it's better. If you can mount it with on long cleat probably better. Two long cleats even better.
I thought you were building a shelf unit as an entertainment center. Your using a adjustable shelf system. I'm not familiar with nor does it show how the brackets stay in place. However your going to have 3-4 screws per upright and should have 3-4 latter being better uprights all mounted into studs.#6 screws will work but make sure they are long enough to go 1 1/2" -2" into the stud. Real plaster walls generally have slats over studs for the plaster to adhere to. The slats are generally 1/4"-3/8" thick with 3/8" - 1/2" of plaster depending on who the plasterer was and how straight the wall was.
As for the long cleat, I should have said French cleat. However that don't matter since your not building this entertainment center.
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