I think chords at least three notes played at once, with the exception of maybe power chords. Using your definition, every piece with two or more notes has chords :)
This may be a pedantic clarification, but that is the definition
In the eyes of the Common Practice two simultaneous notes are not chords; in rock they most definitely are; in EDM you don't even care, since timbre is all that matters; in jazz you'd say "it depends" (e.g. might even be a triad with an omitted 5th... depending on context!)
Music theory is too post-hoc.