"Hecate II, because of its huge size and weight, a fearsome amount of STR setting was required. Sinon as a sniper had her STR higher than AGI, so she was barely able to equip it. " AGI based yet has her STR higher than AGI? Logical...
In many RPG's people can make a build to get the nessasary items and then go along with the other stats as and when needed.
While yes the Hecate II requires Str, it's entirelly possible that she put her Str just high enough to hold the ammo, weapon and such so she doesn't suffer a movement penalty and then enough AGI and such to be an effective sniper.
I mean how else would she have beaten Behemoth if she were entirelly Str based? I'm going from the assumption that without AGI it becomes harder to evade enermy bullets and what-not.
I'm going to repeat this... "Sinon as a sniper had her STR higher than AGI". This specifically states that Sinon doesn't increase her STR just high enough to equip items, she focuses on that stat more than AGI.
Not to start any flaming or whatsoever, but I think it would be better to classify her (at least in GGO) by her defensive stat and weapon class instead of the offensive stat like STR as a primary classification.
If what I saw in the anime was right, there was practically an argument that AGI type characters are/have become weak. Since a character's damage in the game was practically decided by the weapon (and caliber noting the FPS elements present plus Shino's flavor text dumping on Kirito) plus where the enemy is hit (among things like DEF and armor stats), it would be pretty meaningless to argue if she's just taking STR for the weight or not as a base for her build.
As quoted above, Sinon has a build with high STR (one knows that heavier weapons like her .50 cal and its ammo (minigun guy had STR too) give a large weight impact).
However, in regard to GGO's play mechanics this (STR) probably doesn't have any direct effect to damage (other than the difference between the guns and ammo you can carry/use).
She's an AGI type with STR to use a large caliber rifle who relies on dodging compared to someone who has high STR to be able to wear heavy armor and weapons plus VIT which in common sense would increase HP, relying on being able to take hits.
It's pretty much either building to "dodge" or building to be "able to take a hit and survive". The STR part is just subject to what she's carrying as it wasn't stated that the guns increase in damage with STR or DEX.
Note: The beam sword Kirito bought was shown to have stated a "caliber" the same as a gun's ammunition on its stats i.e. "9mm, 5.56mm, and so on" on the anime. I don't know if it means the sword has the ATK power of the enumerated bullets or is just able to cut through them.
I do know that GGO's gameplay was portrayed to have factors similar to FPS i.e. a gun's damage output is based on accuracy and caliber + piercing capability as you won't be swinging it around like a knife.
Sorry for the long comment, I just wrote what I observed on the anime.
STR only affects what kind of weapons you can carry. It does not affect damage dealt directly, but it does indirectly as C9 stated.
A-1 is known to be lazy. The Kagemitsu stats seemed to be copied from some pistol, since the Kagemitsu is a one-hit kill kind of weapon, unless you only scratch your opponent's limbs or something.
And for your comment about her build, here's a quote:
Though Sinon's class as a «Sniper» was extremely rare, it was one of these. To equip a large-sized sniper rifle, they have to strengthen their STR status, and then have to increase their DEX to improve their accuracy, and finally a suitable amount of AGI to get away quickly from the scene after a snipe. However, they would lose if they were discovered, so they gave up on VIT completely
Sinon has no use in VIT, since a sniper is not suitable for close range battles. Her strategy isn't to "dodge", it is to "kill before the opponent gets too close". That's why she only snipes a target if she is sure that she can hit him or if she has backup to draw fire. That's why I don't see the point in categorising builds by defense. The characters categorise it by stats.