Hi Buzzerker! I didn't create those Stolen Lands maps, Luckmann made those maps and posted here in the comments! They're quite awesome.
From what I can tell, it looks like they might have taken those full marshland and water tiles and made them into river sections, most likely by adding an overlay and painting a brush over the disguised tiles, leaving that river effect. Looking through the map I can spot a couple of different areas where they may have edited or erased certain parts of tiles to provide the desired effect.
My stock rivers in PH1 match the road tiles and have muddy borders. In my second tileset, the rivers are created exclusively hugging tile borders. You might be able to use some of the coastline/water tiles in PH2 to create a wider river like that, but I think they'd be two tiles wide.
I'm hoping to update this pack sometime this year to make it more aligned with the pixel hex 2 tileset- specifically, creating transition tiles that are half land and then half transparent, allowing you to layer land borders across any type of full tile without having to hunt down the specific tile (for example, the "grass to snow" tile). This would also make it a bit easier to replicate what you're seeing below. I'll look at adding some thicker river tiles that fit within a hex.
Thanks!