It is not an arbitrary redefinition. Most textbook “definitions” of money do not actually define money; they describe its functions: medium of exchange, unit of account, store of value, means of payment.
The MMT tax-credit view is doing something different. It distinguishes money, money-things, and money-functions.
Money is the unit of account: pound, dollar, yen.
Money-things are instruments or records denominated in that unit: coins, notes, tally sticks, reserve balances, bank deposits, and ledger entries.
Money-functions are what those instruments may do: mediate exchange, store value, settle payments, discharge debts.
So “money is a tax credit” is best read as a shorthand. More precisely: state money-things are tax credits denominated in the state’s unit of account.
The state defines the unit, imposes liabilities in that unit, and accepts particular instruments denominated in that unit back in payment of taxes, fees and fines. That creates baseline demand.
The gain is analytical: it distinguishes currency issuer from currency user. Taxpayers do not fund the state with a pre-existing thing the state needs. Taxpayers need state-accepted instruments because the state has made them liable in its unit.
Bank deposits are private money-things denominated in the state unit. They settle tax obligations through the banking system, ultimately via state money-things (tax credits) at the central bank.
MMT observes that the monetary system is a public monopoly. The issuer creates demand by taxation and sets price by what it pays. The constraint is not “finding the money”, but real resources.
(Gold is not money. Gold is a mineral. A gold coin may be a money-thing if it is a denominated instrument within a monetary system established by government.)
MMT/post-keynesian types redefine well understood concepts to prop up their arbitrary perspective. But why is money best understood as a tax credit? What's the economic function they try to capture with this redefining - and why? What's the gain of this new definition?