For the benefit of others, it's also worth pointing out that the author isn't talking about "integration tests" but "integrated tests" (as he defines it).
Integration tests = testing individual software modules as a group/combination.
Integrated tests = instead of testing one behavior at a time, multiple behaviors are tested simultaneously. (or in the author's words: "any test whose result (pass or fail) depends on the correctness of the implementation of more than one piece of non-trivial behavior.")
It is also worth pointing out that the author used to use the term "integration tests" in this post, and only changed to "integrated tests" after writing.
So a claim that these are completely distinct/disjoint ideas is not really supportable.
As far as I can tell, he doesn't explain the name change, but having watched the talk before he changed the name, it looks like "integrated" is a somewhat more general term.
Specifically: if you are "testing individual software modules as a group/combination", how are you going to do that without "depending on the correctness of the implementation of more than one piece of non-trivial behavior."
I see exactly one way: your "integration" tests have to be trivial, really more akin to characterisation tests. "When I hit this external API with this value, do I get this reaction?"
As far as I can tell, he doesn't talk about this in the post, but he does in the talk/video. These are interface/boundary tests. So you test each unit in isolation, and you test the boundaries. If your unit tests are sufficient and your boundary tests are sufficient, plugging things together will work.
So no integrated/integration tests.
Now I am actually not that strict, I let my boundary tests leak a little towards integration/integrated tests, because it is possible to just not hook up the components right. So you want to check that with some smoke tests. However, once they are hooked up, the more complex behaviours Just Work™.
Integration tests = testing individual software modules as a group/combination.
Integrated tests = instead of testing one behavior at a time, multiple behaviors are tested simultaneously. (or in the author's words: "any test whose result (pass or fail) depends on the correctness of the implementation of more than one piece of non-trivial behavior.")
Integration tests are very important.