No, but its formulation seems to imply that there is such a definition, that the US obviously don’t satisfy it but that a lot of americans mistakenly believe that it does.
The definition doesn't exist, but yet, yes, many Americans do believe it still.
If communism didn’t work on its own, capitalist countries wouldn’t need to constantly sanction and strangle those societies, whose goal is implementing it.
If it was a failure, they’d just let it fail on its own. But they never do that.
The only reason the American capitalists fight it so hard, because its success exposes their failure at home.