The use of the term is definitely loose, and moreover the habitual exposition to a sound character that doesn't closely emulate live sound will easily label that which actually does, not least dynamically, as an outlier; a (more) realistically reproduced trumpet, saxophone or drum set at full(er) tilt will have you wince almost, like a voice 'shouting' forcefully, and may appear "exaggerated" to the uninitiated to whom more stale sounding, low efficiency direct radiating speakers are the norm.In my case, 'shouty' refers to sounding 'loud' in an unpleasant manner not related to the music itself. IME when you have all your ducks in a row, a good system will not sound loud even when it is, it will only sound like the music and if that is loud, like a brass fanfare, so be it, but the system does not editorialize. ESLs can do this as well as a few box systems, but so can horns if properly designed. When measured, the system will be found to be low in higher ordered harmonic generation, free from mechanical resonance brought on by microphonics and no weird frequency response anomalies on axis, with gently rolling response off axis, finally with good total room energy (entirely off axis, which must be absent of any high frequency peaks).
Horns can be very nice when interactions with side walls are going to be hard to avoid if you don't have controlled directivity. This is because side walls can have early reflections which the ear interprets as harshness.