If your definition of the supernatural is limited to ghosts, goblins, and ghouls, you could argue that there's little supernatural stuff happening in this book. Sure, there's a ghost, but there's also a logical explanation for that ghost: it's really a parrot. If your definition of the supernatural extends to extraordinary mental abilities, like telekinesis, then Matilda has got the supernatural in spades. To those who don't know better, Matilda's a regular little girl. But as Miss Honey discovers, Matilda's way more than a genius. She's practically a member of the X-Men.
Matilda is so smart that even if she hadn't developed supernatural powers, she would still have been able to save both herself and Miss Honey. She's just that awesome.
The only reason Matilda develops supernatural abilities is so she can help Miss Honey, and once she's helped Miss Honey, she doesn't need those powers any more.