Idempotency is not about "you get the same result", it's about the effects of your http request on the server. Notice that the definition you quoted is in terms of side-effects, not results.
If a request changes the state of the server and another identical request changes the state of the server in a different way, it's not idempotent.
If a request doesn't change the state of the server at all it is idempotent, even if subsequent requests might get different responses (e.g. the stock quote example in my previous post).
If a request changes the state of the server but repeated identical requests don't have any different effect it is also idempotent. For example, DELETE is idempotent because DELETE-ing something N times is the same as deleting it one time.
If a request changes the state of the server and another identical request changes the state of the server in a different way, it's not idempotent.
If a request doesn't change the state of the server at all it is idempotent, even if subsequent requests might get different responses (e.g. the stock quote example in my previous post).
If a request changes the state of the server but repeated identical requests don't have any different effect it is also idempotent. For example, DELETE is idempotent because DELETE-ing something N times is the same as deleting it one time.