I worked with the Bigtable folks at Google. LevelDB's design is ripped straight from BigTable, which was designed with that assumption in mind. I'm also pretty sure it was not designed specifically for Google Chrome's use case - it was written to be a general key-value storage engine based on BigTable, and Google Chrome was the first customer.
RocksDB is Facebook's offshoot of LevelDB, basically keeping the core architecture of the storage engine (but multithreading it), and is used internally at Facebook as the backing store for many of their database systems. I have never heard from anyone that RocksDB was optimized for in-memory workloads at all, and I think most benchmarks can conclusively say the opposite: both of those DB engines are pretty bad for workloads that fit in memory.