I think that only affect uncommon dwarf weapons the part to count as simple weapons.
Using the Orc weapons as an example, The Orc Knuckle Dagger would go from Martial to simple and the Orc Necksplitter from Advanced to Martial.
But I can be wrong.
"Sneak Attack with any Simple Weapon" doesn't involve Proficiency:
The ability works even if you are somehow not Trained in Simple Weapons.
So while DWF lets you share Simple Weapon Proficiency Bonus with those weapons,
it doesn't mean they count as Simple Weapons for purpose of using Sneak Attack as Ruffian Rogue.
There isn't any fundamental change here from how 1E used "treat X as Y for purposes of proficiency".
As DMW says, the battle axe, pick, and warhammer are not treated as Simple Weapons, so will not increase proficiency beyond Trained even when all Simple Weapons do. Conceptually that seems odd and unfair, so perhaps they should also be counted as having Dwarf trait in order to do so. Of course, since not all characters necessarily have Simple Weapon proficiency (Wizards), separately granting proficiency in those weapons is also warranted, although in that case they would not further increase.
I also don't think getting something as a Simple weapon for Proficiency qualifies it as Simple for Ruffian either.
Sounds like an FAQ question... There isn't really any definition of 'simple weapon' so it's be nice to know what the intent was.
Clarification as to whether "For the purpose of determining your proficiency, martial dwarf weapons are simple weapons" type effects apply to things which require simple weapons other than "calculating your proficiency" would be appreciated.
Since it seems like a gnome ruffian with the appropriate feat should be able to sneak attack with a hook-hammer since an elf-thief with the appropriate feat can get dex to damage with a curve blade. But by RAW I don't think that works.