Today's Economic History: Roth is very good on "money" defined as a unit of account.
But there are, of course, other perfectly-fine definitions of "money": "means of payment", "medium of exchange", "that which you need to hold to take advantage of or avoid suffering from market disequilibrium", "even store of value".
To say that the definition attached to how you use the word "money" is the only correct definition and that everyone with a different definition is doing it wrong--well, that's just doing it wrong yourself...
Did Money Evolve? You Might (Not) Be Surprised: "The earliest uses of money in recorded civilization were not coins...: