It does look like it needs relief joints cut to stop the chipping. The trouble with that is they have to go somewhere. I don't know how far you would need to cut to make it work. There are several brands of concrete patching products that might work. Lowes Depot carries Seka products that may work, or Ardex is a more professional brand that we use sometimes. Remember a patch is a patch and always will be. Some work some dont. One trick to keep from making a mess is to clean the area well and let dry, then use duct or wide masking tape to tape off the area so you don’t make the patch bigger than needed.