Citing my authority, I studied music at the University of Washington School of Music for three years and at the Cornish School of the Arts for two years, then put in a year of private music theory lessons with Mildred Hunt Harris. This does not make me another Johann Sebastian Whatsizname, but I am familiar with the terminology used by some pretty heavy-duty musicians and teachers of music. The Grove dictionary's definitions were generally regarded by most of these folks as pretty loose and sloppy. Sorry, but that's the way it is.
To say that two notes sounding together in accord means it's a chord is like Big Bill Broonsy's definition of a folk song -- cute, but not very precise, or helpful in really understanding what's going on.
In Introduction to the Theory of Music by Howard Boatwright, Professor of Music Theory at Yale University, a very comprehensive textbook that covers everything from basic theory to the physics of music to melody writing modeled on troubadour and trouvere harmonies (Middle Ages, back when minstrels roamed the earth), Professor Boatwright says "Two or more notes may receive the general designation 'harmony"; an interval is a harmony. But a 'chord' is at least three notes." He then goes on to say that they must be three different notes.
That's only one book out of my eighteen-inch stack of music theory texts and workbooks, and they all say the same thing. Except the Grove dictionary.
With only a pair of E's and a B, what chord symbol are you going to put to it? It's sort of an E chord, but what kind? Dunno. It takes a G to identify it as an Em or a G# to identify it as an E (major).
And Murray, all it takes to make a diminished chord is three notes: B, D, and F are sufficient. A G7 (and all Dominant 7th chords) contain a diminished triad.
Take a sheet of manuscript paper and write a C major scale: C D E F G A B C. Then write another scale, E F G A B C D E, directly above the first one. Then another scale, G A B C D E F G directly above what you already have. The triads (chords) you now have in sequence are C Dm Em F G Am Bdim and a repeat of the first C an octave up, all the triads available in the key of C major. Add an F above the G chord or slide a G under the Bdim and you have a G7, the Dominant Seventh chord in the key of C. When you have four, five, or six notes in a chord (unless you are going for ninths or eleventh chords, which is more complicated than I care to get into here), you are merely doubling notes that are already in the triad.
Whew! Hope this helps.