What would you consider a "furry video game?" Can it be any game that has anthropomorphic or talking animals? Or does the world need to be based around them akin to Redwall, Zootopia, etc and have no humans? Would something like Donkey Kong Country or Banjo-Kazooie be classified as furry video games? Anyway-
>Solatorobo
Haven't played it myself personally, but I see a lot of people talk about Solatorobo, it's the first thing that came to mind despite not playing it or even knowing what it's about.
>Inherit the Earth
It's a fun little classic point and click adventure, it's also been rereleased on Steam. It's not all that difficult or challenging but it does have some neat concepts, visuals, and dialogue. Character interaction is it's strongest suit, but there's not a lot of differences between the animals aside from personality and design. Sometimes they can seem like reskinned humans, the worldbuilding could be better, there's potential for more games in that regard. Or at least it would be nice to see more games like this.