Yeah it’s exactly what it is in the definition you gave. The western form of music, and yes there is other music that isn’t built on this form or tonal music. Examples are Chinese music, African tribal music, anything that is not western or diatonic. The difference between western music and other music is western music has harmony, chordal structure, and strict time signature. Other cultural music only has melody, like a Indian song where there is only a melody, no chords and no harmony. With western theory you can harmonize it and put chords to it, but traditional Indian music does involve these principles. Time signature can easily be differentiated between Tribal music and western music. Tribal music will usually have a sequence of measures like 5/4, 7/8, 5/4/, 3/4. Where western music will normally stick to one signature. That should answer your question.