Pete, that pictured Arlington TV box is designed for shallow residential basement walls, with only furring strips between the drywall and the concrete.
drvbysound, bringing bundles down from above, for a rack, is much easier than from the side or behind, if it's a pull-out. False ceiling (drywall, but dropped, with an access panel) in the closet makes it easy to add more cables later, from a side wall.
Bundle comes down from ceiling, with ~3-4 feet of slack. Bundle then fastened to top back of rack, and individual cables routed. Rack on casters can then slide forward, out of the closet.
The Arlington Decora scoops look nicest, but not the cheapest. Easy to retrofit a 2nd double gang scoop, in the future, right next to the first, if needed.
Which rack are you considering? Sanus preconfigured is pretty darn cheap. That closet is pretty shallow, at 24". If you can turn the rack sideways, and step into the closet to access, a fixed rack will remove many of your headaches, will give you a few more U's of rack space, and save money.