A project to make this real would be a large undertaking. I'm not going to say 'massive' because it's not hellishly difficult, and I'm also avoiding the use of the word 'impossible' because given enough time, this could certainly become a reality.
However, this will take patience, sweat, blood, and quite possibly tears as well, not to mention that there's a few problems right from the get go in trying to achieve a 'realistic' look.
One: The FeralHeart models are low poly. By low, I mean the models themselves have a poly-count of about 5000 triangles; you could put these in a mobile game if you wanted.
Because of this, the model deformation is not as smooth / tidy as one might expect from a more recent game. If you want good looking animations without clipping and weird torso, shoulder, and neck areas, then you'll have to replace the current model with one that has a higher polygon count around the chest and upper torso region.
Two: The rig / skeleton was built with quadrupeds in mind. FeralHeart is an animal game and the animals that it emulates are quadrupeds. The 'rig' (I use that term loosely, since it's more of a skeleton than a rig) is a quadruped rig.
When trying to make quadruped animals behave like bipeds in animation, you would usually have two different rigs that you switch out when needed, or make a specialized rig with you specific needs in mind, like Alex the Lion from Madagascar, who uses one rig that allows for performing bipedal and quadrupedal animations.
FH doesn't have such a rig, that's why it's hard to make bipedal animations look good with it. Especially since the joints / bones are placed and joined like a quadruped's.
Third: The weight painting needs to change. If you're going to change bone placements, then you'll have to change the model's bone assignments, otherwise it'll look like a mess. Again, not impossible... just a pain to actually work through.
Aside from that, if you're looking for the mod that Kuri mentioned, I believe it can be found here: Felines (http://semi-illit.tumblr.com/post/126452502529/its-here-i-call-it-furry-heart-aka-furry-hell), Canines (http://semi-illit.tumblr.com/post/127756559434/the-moment-youve-all-been-waiting-for-furry).