> I think they mean existence in general, not the existence of any specific thing.
Yes, but the definition of "existence" doesn't require that anything must actually exist.
In other words, it is not the case that existence "cannot not exist by definition."
> Meaning that if there were no “existence” then we wouldn’t be here to consider its nonexistence.
That's an anthropic principle argument, which is not an argument from the definition of existence. One of the premises of that argument is that we exist already.
