However damage is calculated one thing is for sure, there is a very wide margin in damage.
In the third attempt (on Pomburner) notice that Archer 2 only used Heavy Shot twice. It did not have the highest max damage, but merely the highest average damage. That average is skewed because again there are only 2 heavy shots from Archer 2 that fight.
On Whiskerwall Archer 1 is clearly ahead. Yes there are still some areas where it is inconsistent, but far less than in support of DEX/PIE.
Based on quick testing on patch day I did not feel it was worth testing STR at this time.
Also what the chart says is that Attack appears to play more of a factor the higher the defense the mob has, and that in general it appears to be more consistent with higher damage (when controlled for outliers caused by the wide margin of the damage formula)
That is because you are focusing on the wrong numbers. Your total damage will be skewed if for example you hit Wide Volley and hit a bunch of Moogles (unintentially even), this contributes little to the fight unless as a group you are fighting them this way. The moogle will likely regen, and that extra damage and DPS you show overall may have actually meant very little.
This is not a comparison of DPS or Total Damage, this is a comparison of Max and Average damage. It is unaffected by how the scenario unfolds (except where you see invalid where I've had to invalidate Average results due to an archer hitting an immune Balloongle).
None of the abilities were used with buffs, there are no debuffs which could affect them. They are fighting a unique enemy (which should have identical stats every time), and they are wearing the same gear between the attempts. They are all using Ifrit's bow, with Cobalt Arrows.
The number of attacks is noted alongside the averages so that you can tell if the sample is smaller than usual (explaining inconsistencies in some areas).
I have seen very little so far to support that hypothesis. As you see Archer 1's average light shot was higher in both fights with an Attack build.
Most people are testing theories on normal mobs. However if there are checks comparing the player against the mob, fighting a mob lower than you (with a much lower defense than your attack) would likely not show how useful Attack Power actually is in encounters that actually matter (which if we are talking about Parses generally means endgame encounters).
They may be encountering either the aforementioned issue with the large damage margin on attacks, or hitting the damage cap *which is possibly tied to weapon damage* (assuming there is one, and I am as a member tested it using Dated Red Coral Arrow and hit a max of 906 in damage with 15 additional points in both DEX and PIE alternatively).
Again I realize my sample is too small to draw definite conclusions, and I'd encourage others to contribute to the discussion with similar data to see if they can verify it. However, parsing against normal mobs means nothing to an endgame archer if it can't be verified that those results/conclusions actually translate to endgame encounters.