I’d say that some of the differences in opinion here are likely arising from different goals in visibility/representation. Is the goal of the “nonbinary visibility” meant to benefit nonbinary readers, and provide possibility models/characters to see themselves in? Or is the primary goal of the representation to educate others and provide a kind of “nonbinary 101”? The strategies used in depiction will be influenced by the author’s goals with the character.
If the game is being written primarily for an LGBT audience, who likely have familiarity with these topics, it becomes easier to approach the topic with nuance, and a wider range of the full breadth of (incredibly diverse) nonbinary experiences can be explored.
If the game is aimed at more general audiences, though, introducing the reader to they/them pronouns or neopronouns can be valuable. The author may have to sacrifice some of the more nuanced aspects of nonbinary identity for the sake of clarity. (I’ve been working on balancing this myself, as a nonbinary author writing a game with major characters who are nonbinary).
That said, I’d argue that, even if the author indends their work for wider audiences, there is room for nonbinary characters who use “she/her” or “he/him” pronouns. Educating readers that there are nonbinary people who use those pronouns has value. Pronouns are perhaps the most obvious way to indicate the character’s gender, but there are others ways, as have been discussed. Gender presentation, having the character discuss gender identity if the topic comes up in conversation, etc. Just as in real life there are many ways to be nonbinary, I think there are many ways these games can effectively convey nonbinary identity to the reader.