I'd like to answer your question but first, I want to remind you that I'm not a pro, so after you read my answer I suggest you do some more research based on your understanding from my answer to find out about the more advanced tips tricks and knowledges on texture painting. I'm currently learning this style as well.

I believe it's hand painted texture (or texture paint). I've seen a lot of high quality hand painted texture style and they are fking amazing. But it seems this particular game doesn't have much texture detail on them. As you can see the cube stones and the grass are all in one flat colour. Green, and that's it. Light brown, and that's it. No gradient, just so little scratches, (almost) nothing. It almost like they just applied Diffuse BSDF material and didn't do any painting.
The objects with the most texture detail on them are the metal box and that structure on the left on the second picture, as you can see they have chipped paint detail.

Here's an excellent video to follow if you want to start texture painting.

I hope this helps!