Interesting how this term is used so widely in audio these days, without definition. My initial though on when I read this is that it would be more around the 1-2k area. A quick rough search had some saying 1-2k, 2-4k, and even 4-8k (I think that last one is way too high—really hard to get anything resembling a shout out of 6-8k! Are they thinking "shrill"?).
"Shout" is a vocal property, so I'll start there. I realize "shouty" might be defined more a property strong harmonics as opposed to the fundamental, but it might help to relate the fundamental to the piano, and then consider the first few harmonics as integer multiples of that frequency. Sting's "Rock-san" is 440 Hz, so the next harmonics are 880, 1320, 1760, 2160... Now, I think that note, yelled, is more screech than shout, but I'm start high on purpose. A high shout for me is closer to 300 Hz (600, 900, 1200, 1500, 1800...), so that 1-2k is not looking bad to me—for my idea of "shouty", at least. That would translate into a loud and wide-open-mouthed shout that boosts some of those mid-range harmonics, beyond what you'd get with a normal voice.
I'm not saying you're wrong, just that this is such a subjective term. On the one hand, I would say that from my experience mixing vocals, up near 6k is where I might want to boost for articulation, and there doesn't seem to be much oomph there. On the other, if it's broad enough and strong enough boost 4-6k, I can understand why you might think of it as shouty—it would be like someone who is exceptionally close to your ear, and loud.
Obviously, stating frequency ranges is less ambiguous, but that's not such an easy call for people who don't spend a lot of time with audio signals and filters.