You are indeed right it is InventoryIcons.json not InventoryIcons.data. That was a typo sorry.
The json file does indeed contain more information than needed when made using TexturePacker, but that should be fine it only uses the parts mentioned in the post atm.
I did notice a couple of other typoes in the instruction part of the plugin, and I'll fix them later today and make a small demo.
I am sorry for the inconvenience. If the inventory does not show up in the game then it is most likely caused by the plugin catching an exception.
Which version of RPGMaker MV are you using? I am pretty sure I have some code which is only working on version 1.6.1 or newer. If you are using a previous version let me know and I'll make a compatible version. :)