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Question — how often does this really happen, and how often does it happen outside of a JRPG?
I'm sure most of us know that in Final Fantasy VII, Barrett and Vincent primarily use firearms and yet do more damage as their strength stat increases. But this is also a JRPG where things are a little abstract anyway, and maybe they can hold their aim steadier or control the recoil better.
Likewise, Momo in Breath of Fire III uses a gun (well, more like a 12-pounder cannon
that she shouldn't be able to lift...), and has a strength stat. Another JRPG, and same deal.
In most cases, you could usually say that any damage increases from level ups are from landing shots more precisely because it's easier to carry and maneuver the weapon.
And in many other cases (Fallout), having 5 or 10 strength has zero difference on how well you fire a pistol.
Edited by KD
Maybe One Stat to Rule Them All?
I don't know that it happens much outside of JRPGs and other games with JRPG-inspired RPG Elements, but I think it probably happens often enough in those games to be tropeable. I can think of at least three western RPGs which do it: in Tyranny and both Pillars of Eternity games, Might is more than physical strength, and affects damage on all attacks, including spells. The Pillars games very much run on Soul Power and were very consciously trying to avert Dump Stat, so The Six Stats overlap less than in traditional D&D.
Edited by Unsung
Player character being more powerful somehow makes the same gun(or any weapon that shouldn't be logically affected by the wielder's own ability) does more damage.