Is merkle tree a must in any blockchain?

[TheLuckyBastard]

Some modern blockchains don't use the classic merkle tree or use something like DAG.

I was given a YellowPaper of a really exiting project for review (I am under NDA, so I can't tell the name now).
I loved everything but the absence of merkle tree rised questions.

Instead of the merkle tree they link new transaction to last transaction to adress and block number where it happened.
So they are kind of a hybrid between DAG and classic blockchain.
They justify it by dramatically increased speed of confirmation and transaction amounts per second.
All transaction history can be still retrieved from decentralized network storage and checked.

Do you think such proof of funds is valid?