HTTP already handles this just fine if you have sensitive forms: your form can include a one-time token which your server validates. If the token has already been used, you don't process the second request. What we definitely shouldn't do (as the author suggests) is disable form submissions on subsequent clicks. What if the first response fails? You'll have to enter the entire form all over again, instead of being ab…
In fact, the same technique should apply to session tokens in general. They should be signed by the server, which removes the need to do I/O to filter out unauthorized sessions and mitigate DDOS attacks.
So yes, this is the correct way to do it. But additionally, I don't see why it's so bad for the client to prevent quick submissions in succession... maybe disable the button until the response comes back, with a 1 second timeout, and alternate suggestions on repeated failures.