Do you have Selling Manager or Selling Manager Pro? The listing appearing at the right is a quick view (and is new), but any changes still have to be saved and submitted. (You can also close the preview if you prefer).

Just in case it helps, when you bulk edit the categories by selecting all the listings you want to change, then, in the edit view, select all listings again and click Edit Fields > Categories. This window pops up, and you only want to change the second two (Store Categories).

Your existing store categories should be in the dropdown menu.

After that's done, click the blue 'Submit Changes' button at the bottom of the screen - it can sometimes take a few minutes for the listings to actually be moved to their new categories if it's worked.

Alternatively, you can revise a listing individually - the store category options are at the top of the page, just under where it shows the eBay category you've selected, and pulling up the dropdown menu should give you the option to select from your store categories.