We aren't a Nintendo 64 emulator, so this texture pack won't work with us.
It won't work right out of the package, but you can make it work.
All you just need to do is enable it to dump the textures (Graphics > Advanced > Dump Textures), boot up Super Mario 64 Virtual Console, and play the game as usual.
Once you think you have gotten enough textures, you can copy all of the dumped textures into the load folder (Documents\Dolphin Emulator\Load\Textures) and replace them with the Super Mario 64 texture pack by copying the dumped texture's name, going into the texture pack, and replacing the texture file with the dumped texture name.
Afterwards, you enable it to load the textures (Graphics > Advanced > Load Custom Textures), and play Super Mario 64 Virtual Console.
Do I have to play the whole game to dump all of the textures?
Unless they're recycled a lot, then yes. Dolphin can only tell for sure that something's used as a texture when a game tries to use it as such.
Is there a 100% guarantee that the texture will work?