I only have 2 months experience with pathfinder, but no one else has posted yet so I want to at least contribute!
In conjunction with the Ruffian text you included, here is the Pick Fatal text:
Fatal 1d10: The fatal trait includes a die size. On a critical hit, the weapon's damage die increases to that die size instead of the normal die size, and the weapon adds one additional damage die of the listed size.
I think as written I agree that it feels pretty clear that the Ruffian would no longer get to apply sneak attack damage, as the damage die of the Pick is no longer a d6, and thus does not meet the Ruffian requirements.
At the table though, I would totally understand allowing it! (though idk how that affects things game balance wise in terms of weapon choice for the Ruffian, and subclass balance against the other Rackets)
If you want to get super wordy about it, I could see an alternate argument. The Ruffian thing says to apply any abilities that alter the die size first, but it's a weapon trait that is changing the die size. With my brief system experience though, I have no idea if it's stated somewhere that 'abilities', as referenced in the Ruffian text, are just meant as a catch-all term or if 'abilities' in this type of context specifically means some kind of ability that you choose to apply.