Ignoring the discussion about tonal centre, which I find confusing and strange in the OP question (or in really in the guitar mag referred to), I end up with pretty much the same as BigDaddyLoveHandles.
An interpretation of the written material could be:
1. Major tonal centre one step lower than a dominant7 situation.
Playing e.g. F major scale over G7 would imply that a play a G dorian type scale over the G7. Bluesy and great … at times.
2. Major tonal centre one step lower than a minor7 situation.
Playing e.g. F major scale over a Gm7 is the G-dorian scale. The tonal centre would be F, and you would really be playing F major
3. Major tonal centre a fourth higher than a dominant7 situation.
A forth higher than G would be C. Playing C major over a G7 imply a G-mixolydian scale. The standard choice for a dominant 7th.
4. Major tonal centre one semitone higher than a minor7b5 situation.
C major scale played over a Bm7b5. Locrian scale.
5. Convert a minor7b5 to a 9-chord (root becomes the 3rd) and use ideas from 1, 3, 10 and 14.
Bm7b5 converted to a 9-chord with the root as the third will mean that the chord you are really thinking about is a G9. Playing idea 1 would be tricky, and would not include the root of the original chord (Bm7b5), but I’m sure it could sound good. Playing idea 3 would be just like playing idea 3 as far as I can see.
6. Major tonal centre a fifth higher than a major7 situation.
D major scale over a Gmaj7 chord. Lydian scale!
7. Major tonal centre, which is the same as the given major7 chord.
G major scale over Gmaj7. Ionian scale or really the major scale itself.
8. Major tonal centre a minor third higher than a minor7 or dominant7 situation
Bb major scale played over a Gm7 is the G-aeolian scale or G-minor scale.
Bb major scale played over a G7 is still the G-aeolian scale or G-minor scale, but will have the blues in it as the minor 3rd is included. Interesting. Must be tested.
9. Minor tonal centre a major third higher than a major7 situation.
B-minor scale played over a Gmaj7 chord: B-minor scale is the same as D-major scale. Hence, this is exactly the same as idea 6.
10. Minor tonal centre a fifth higher than a dominant7 situation.
D minor scale over a G7 chord. D minor scale is the same as a F major scale, so we are talking idea 1 again.
11. Dominant7 tonal centre a fourth higher than a minor7 situation.
I guess this means that G mixolydian scale is played over a Dm7 chord. If that is true, this is just becoming confusing. It is the C major scale, or D dorian scale if you prefer.
12. Major tonal centre a minor third higher than a minor7 situation.
This is already mentioned in idea 8.
13. Major tonal centre a minor sixth higher than a minor7 situation.
A minor 6th higher than g is Eb. Playing Eb major scale over Gm7 would be the Phrygian scale.
14. Dominant7 tonal centre a b5 higher than a dominant7 situation.
Playing Db mixolydian over a G7. Standard tri-tone substitution.
A confusing way of presenting it, and not very good in a theoretical sense, but maybe it can be helpful. They all seems to be workable substitutions.
It's getting late here, so I'll check again tomorrow.