I don't think the paper is talking about the persistence layer. Rather it's focusing on the cache layer.
From the paper:
"Modern internet-scale services often rely on remote, in-memory, key-value (RInK) stores such as Redis and Memcached. These stores serve at least two purposes. First, they may provide a cache over a storage system to enable faster retrieval of persistent state. Second, they may store short-lived data, such as per-session state, that does not warrant persistence."
If you look at Fig.2 in the paper, the database (persistence) layer is always there. What the paper is advocating is to move from an out-of-process cache server like Redis to an in-process cache library like Java Caffeine