While I haven't had a chance to play the Fractured But Whole yet, after reading the article I don't see anything that is particularly transphobic, at least not in the sense that it sets trans people apart from everything else South Park does.
It's important to remember with this sort of thing that Trey Parker's intention is rarely to mock individuals (public figures aside), and is virtually always about mocking the current political and cultural climate, primarily issues of political correctness. For instance, I've been filling out some random applications lately, and was struck by the number of "gender" options on forms now. I believe that it is this cultural change that South Park has targeted, not transgender individuals. Likewise, the variety of dialogue from NPCs reflects the variety of real reactions people encounter, just rendered in South Park's style, reflecting the culture.
I think the article also does a disservice by focusing on what are clearly video game mechanics as indicative of any statement on trans issues or which may represent a failure to explore them. For instance, the first encounter it speaks of is clearly a tutorial battle. Are cis-gender characters just not supposed to have a tutorial fight? That'd be stupid. A lot of the pronoun gendering would require more direct experience to comment upon, but I'd hazard a guess they were running up against budgets and deadlines (Obsidian is really, really, really bad about that) and didn't have time to flesh out consistent FTM vs MTF dialogue so just used the most generic gendering for "other" characters. I would also point out that choosing simply male or female would use the appropriate gendering regardless of being trans, and works perfectly fine for anyone with a binary identification, leaving the problem being mostly an issue of non-binary representation. And I don't mean to sound like I'm separating people who are non-binary from binary trans individuals with this, but simply pointing out that the problem may lie in a different direction than simply being transphobic in general. Unfortunately, even for people who accept transwomen and transmen, non-binary is still a hard thing to swallow or understand.