The example you linked for the guitar chords shows the song in the key of B-flat (Bb) given the capo on third fret instruction. The only chord in the song that at first glance may appear to not fit into the key of Bb is the Ab (F chord played with capo on 3rd fret). Also note that in the key of Bb it is considered more accurate to refer to the G# chord as an Ab chord (played exactly the same). But I will explain what is going on with this seemingly oddball chord.
When selecting chords for a song in a major key, you will most commonly choose from a chord set that includes the following chords (often notated as I-ii-iii-IV-V-vi-vii{dim}).
1) The tonic chord (the key) as the I major chord
2) The chord corresponding to the second scale degree (known as the "supertonic") will be a minor chord (ii minor).
3) The chord corresponding to the third scale degree (known as the "mediant") will be a minor chord (iii minor).
4) The chord corresponding to the fourth scale degree (known as the "subdominant") will be a major chord (IV).
5) The chord corresponding to the fifth scale degree (known as the "dominant") will be a Major chord (V).
6) The chord corresponding to the sixth scale degree (known as the "submediant") will be a minor chord (vi minor).
7) The chord corresponding to the seventh scale degree (often referred to as a "leading tone") will often be a diminished chord (vii-dim).
However, it is common in popular western music to substitute a flattened seven MAJOR chord for the diminished seven chord in a major key. Thus instead of an A diminished as the seven diminished chord often used in the key of Bb major, you can substitute the flattened seventh degree chord which in this case gives you the Ab major chord (A flattened = Ab). If you were in the key of G (as indicated prior to capo in your link) the 7th scale degree of the key of G is F#. So instead of an F# diminished you can substitute an F major (flattened F#).
The flattened 7th degree chord serves as a "subtonic" as it relates to the scale verses the diminished seventh acting as a "leading tone". Here is what Wikipedia says: Wikipedia - Subtonic
"However, while, "the leading-tone/tonic relationship is axiomatic to
the definition of common practice tonality," especially cadences and
modulations, in popular music and rock a diatonic scalic leading tone
(i.e., ♮\hat 7-\hat 1) is often absent.[6] In popular music, rather
than "departures" or "aberrant," the "use of the 'flattened' diatonic
seventh scale degree...should not even be viewed as departures".
For a more in depth discussion of the use of the flattened seventh degree as a substitute for the more typical seventh diminished chord click here Use of bVII in major key chord progression