In addition, as we understand from this myth, from long ago gods who did things like laugh, get angry, and fight like human beings, were an approachable presence to the Japanese people.
Yep sounds good to me ^^ for the last part, maybe something more like “easy to relate to” could be a good translation? (親しみやすい存在 — lit. “an easy to be intimate with existence”)
So these gods from long ago who do those types of things like humans (laugh, get angry, fight) were thus easy to relate to for the Japanese people