Did you already try on Wii ? does it work on wii but not vWii ? do you know how it should look when games are "displayed" ?
because they don't really appear in the system menu, the extracted games needs to be "mounted" into the "disc channel", one by one, from a hidden menu of neek.
it's just to be sure you know you have to press 1 (or 2, I always mix them), and choose the game from the list.
Like you said, neek is not running if there is no extracted game disc found, and seeing it's booting it means it's properly detecting them.
You need to choose the game to mount in the disc channel using the Disc Interface (DI) emulator.
Once you chose a disc, it will appear in the disc channel, and you'll launch it like if you just inserted a read disc in your console.
If you knew you have a hidden menu with a list of games, and it's in that menu you don't see any games, then I don't know how to help
try on Wii, see if it works, maybe it's an issue on vwii only ?
Maybe WiibackupManager is not extracting in the proper format ? or in the proper folder tree, or missing files (most probably!!), compared to DiscEx.
I suggest you use DiscEx once on a game and see what's generated, copied, the folder structure, etc.
I think there are files you need to copy and/or rename from the launch partition into the titleID folder.