They're unrelated, and to each other. That is, you could watch Edgerunners II before Edgerunners and it wouldn't matter. They're unrelated, as is the book V narrates the audiobook for. "No" something, I forget. And the game is unrelated to all of it.

Though, there are similarities. Edgerunners II starts with some gonks (idiots) stealing a computer chip from Arasaka, a corporation based in Japan. The game starts similarly. But they aren't the same story at all.

If anything, you might wanna hold off on the game until after the series, because the game has added elements of the series over time. You can find references and do things related to the series, which implies the series takes place before the game. But none of them spoil the others.