Nice try, but I explicitly stated I was talking about Marxist-style socialism, which is what 'communism' has come to mean. I almost never see people talk about "real" Marxist communism anyway.
Most ideologies and political or economic ideas have had their names subverted to mean something different by opponents (democracy, republicanism, communism, anarchism, capitalism...). That doesn't mean that if you speak in the "formal sense" you can decide to use whatever meaning you prefer.