I don't see any account numbers, unless the handstamp on Lincoln's check contains his account number? How would banks have figured out which account needed to be debited?
Aside from the accounting/routing numbers on the bottom of modern checks, I’d say they’re practically identical.
As far as knowing which account to debit, that’s an interesting question. I guess the banks knew who had which account since there were more face-to-face business dealing.
I clearly remember writing checks in the 1960’s when no account numbers were used. The accounts were held in the holder’s name. Signatures were checked to verify the account holder if there were any questions. Usually the bank teller knew the customers.