That doesn't sound like a complete definition of the term "AGI", unless you mean that anything reducible to a Turing machine is an AGI.
In any case, I'm not sure why the term "artificial general intelligence" should be constrained to Turing machines. Nothing about it implies a Turing machine; just that it possesses intelligence and is artificially manufactured.
In any case, I'm not sure why the term "artificial general intelligence" should be constrained to Turing machines. Nothing about it implies a Turing machine; just that it possesses intelligence and is artificially manufactured.