Even with this extended definition, your argument fails the most important criteria for genocide with the UN definition which is:
The intent is always hard to prove. But I am glad that you agree that the only difference would be the intent ;)
Yet, if you read about some cases, you might see that the intent was not always proven or obvious, and some cases are considered genocide even without intent. For instance, take Holodomor, which is being more and more recognized as a genocide, even though unintentional. But I am happy to talk about other cases.