You may be interested in another paper[1] by Sompolinsky and Zohar describing block-trees rather than block-chains as a better structural approach.
The ledger would still be a chain of blocks.
For real tree like blockchains there are a few examples such as IOTA, raiblocks and byteball.
Do you know if anyone is working to implement something like this?
https://medium.com/@avivzohar/the-spectre-protocol-7dbbebb70...