What you say about the chord tones in the G11 chord is correct.
G B D
F A
C = 1 3 5
b7 9
11
However, he is referring to an F
chord over a G bass note.
Since all the notes are a third apart, we can see other "smaller" chords within the 11 chord.
For example:
G B D
F A C
We see an F Major chord on top of a G Major chord.
The b7 9 11 of G11 is also the 1 3 5 (F A C) of F Major.
In Example 2.13, you have A C F at the end, which is an F Major triad. (3 5 1 = 1st inversion)
G A C F.
An F chord over a G.
Though the G is not played in the chord at the end.
When he demonstrates the G11 cord he does play G in the bass on the 6th string, the F on the 4th string with his pinky and the A, C & F "normally".
So he is actually playing the 4 string "open" F with a G in the bass. (5th string muted)
In all 3 examples he gave, G11, C11 & E11, the b7 of the 11 chord becomes the root of a second triad on top of a lower one.
F chord over G, Bb chord over C and D Major over E.
G B D F A C
C E G Bb D F
E G# B D F# A