Down The River's Edge doesn't do anything novel, or special with it's storytelling.
Tale as old as time, lover's old as rhyme or however the Disney song goes, I sure as hell can't remember.
The geniunity(is that a word? it should be) of the lovers feels right, an ambitious youth, an old and gruff veteran with a heart of gold. A sin that's seems unforgivable, you know the drill.
The story is touching and has enough tension for you to also tense up while reading. While the deer character could have been presented as more gruff (the part where he cracks up was supposed to be a special situation, but he never really seemed as rough as the narrative tried to sell me) everything else was solid.
I loved the extremes the lawman's sprite went for in the end, really showing a completely different side of what was presented at the beginning of the story.
What obviously sells this one is the presentation. Custom UI, backgrounds, animation, comic sequences. The devs hopefully all got treated to something nice after the entire project. I even expected voice acting during the pretty well done sex scene, though that one felt a little too modern for me in the writing department.
Other than that, the sweet ending was earned and felt great. My only real point of critique is the way a lot of the sprites look a little too glossy, but that's just an artstyle thing I personally don't enjoy.