-- HOW TO GET THE EXPANSION PACK --

[Tanshaydar]

I never used Steam so sorry if this is the noobiest question to imagine - but couldn't a Steam user simply upload the new files he got with the update somewhere for Frictional store version users to copy these into their game folder?

Are you asking for illegal content share?
And no, Amnesia.exe has a few new things in it, and it works bound to Steam, which means you need to have updated exe and it needs to connect a Steam account.