Well, that's a big question. Existentialism covers a lot of ground but it's basically the idea that meaning comes from choices made by the individual as opposed to coming from God or society or from reference to an outside authority. There are religious existentialists but for the most part it's a secular approach to life and the meaning thereof.
Phenomenology is an epistemological approach -- a system of knowing how we know what we think we know. Again this is like down the rabbit hole in terms of explaining it, but it's about seeing the world as it is, as a subjective experience, but one stripped insofar as possible of presuppositions.
That answer would earn a solid "-D." But we're throwing it out there just as background for people who are reading this and think WTF?
Basically we're saying that we wanted to show the experience of being in animal morph with as much truth and as little assumption as we could, not in some cutesied-up, anthropomorphic, Disney way. We wanted to create a universe that was independent of God or other external authority. We wanted rational answers. We wanted characters to face decisions between life and death, not between this type of existence and some theorized alternative. We wanted to face moral choices squarely, to lay the alternatives out for readers and leave them to reach their own conclusions. We didn't want to become self-appointed moral or philosophical authorities, we wanted to say, "Look, here's the situation, here's how this character handled it, now you decide if it was right or wrong." We mostly avoided mysticism or the supernatural.
Probably the most basic thing for us was letting readers make basic decisions about right or wrong. We tried to avoid preaching for the excellent reason that, who the hell are we to be preaching? We didn't always succeed in keeping our mommy/daddy voices out of it, but we always intended to make you, the readers, responsible for deciding the right and wrong. So you could say we were inviting you to be the existentialists.