So I think that your original non-hierarchical secret sharing variant makes more sense, relative to hierarchical variants. One of the most common use-cases of BIP32 is just a personal wallet where you don't need to decrypt your privkeys to derive more public addresses, and there the non-hierarchical variant is fine.
I don't understand what non-hierarchical variant you are talking about? Everything in the abstract and the OP refers to a hierarchical (HD) wallet.
The title of the short paper says "hierarchical", but it actually only specifies the non-hierarchical variant of the OP of the 2011 thread (
https://bitcointalk.org/index.php?topic=19137.0), without chaincodes.
With an hierarchical variant you can delegate the root of a sub-tree of the wallet's hierarchy to a third party, without giving this third party access to the other branches of the tree.
The paper quite clearly claims to introduce a new hierarchical wallet. It claims to solve problems that other hierarchical wallets have.
I agree with you that the paper doesn't actually specify a hierarchical wallet.