Does a horizontal cable manager replace vertical cable management?

Not generally. Horizontal and vertical management deal with different axes of the same cabling problem.

The horizontal manager controls the route across a patch panel, switch or group of rack units; vertical management deals with the longer journey up and down the cabinet.

Larger installations often benefit from both.

In a small wall cabinet, however, constructing an elaborate vertical-management scheme can become more cumbersome than the handful of patch leads it was meant to tame, so the scale of the solution should still match the scale of the rack.