It seems that usage varies:
Chord:
"A group of (typically* three or more) notes sounded together" (various Oxford dictionaries);
"The simultaneous sounding of two or more notes" (Grove Concise Dictionary of Music);
"Any combination of notes simultaneously heard can be called a Chord" (Scholes Oxford Companion to Music).
A Triad is a chord of three notes, being (to simplify) the root, third and fifth of a scale; I have seen the analogous
Dyad used for a chord of two notes, but not often. More frequently, just the interval is mentioned, as in saying that a piece ends with an open fifth - Hindemith, for instance, follows this usage in his "Craft of Musical Composition" (page 57, for example). Harmonically, of course, two-note chords are essentially uninteresting, not least because they have no inversions.
*
Note, "typically", not "necessarily"