I am not aware of any such implicit connection of ledger and commutative property, also couldn't find anything as my google-fu is letting me down. Anything I can refer to? Generally curious to know use of term ledger outside of accounting and blockchains.

I have seen it used to mean WAL before, so I am taking this with a dose of skepticism.

In a double-entry ledger the order of transactions doesn't matter, the balance is the sum of entries.

Depending on the data model of your log, if calculating the current state is a commutative operation, I think it's fair to call it a "ledger".