I've worked a little bit with blender and graphic design. I haven't worked that much into implementing these skills into godot, but I'm trying.
From what I can gather, the models have a similar design to other games like borderlands. Its almost like they are painted on, and outlined by a pen.
They make good use of the color brown, as it highlights the other colors in the scene such as green and red.
The scene also fades into a fog/haze with distance.
What I can recommend is looking into shaders with blender, particularly one called a Toon Shader:
https://www.youtube.com/watch?v=bViS42E8Y4M
After getting familiar, move on to applying that to objects in Godot. I found this video that might help, however its from Godot 3.
https://www.youtube.com/watch?v=1duRtTEc2SU
From there, I think its about adding the actual texture art to the models. For me, that means getting comfortable with UV Maps. Here is a video explaining the process for Blender
https://www.youtube.com/watch?v=iwWoXMWzC_c
How to get this particular grundgy/dirt texture, that depends on the brush you have. You can download a ton of them online, and Id recommend finding something earthy or concrete. https://www.artstation.com/marketplace/game-dev/brushes
But one thing that's for sure, is that you are going to choose a shade of brown, and use it for almost everything in your models. So remember that color code (ie black = #000000 and white = #FFFFFF). Maybe something like #967969.
From there I believe the lights and haze you add to the scene will make the difference. Anything that isn't brown will stand out, and make the players bee line towards it. I think this will probably be the easiest part, but I could be wrong. Heres another video:
https://www.youtube.com/watch?v=ogtDKlTnnqo