Even joking racism is still racism. The fact that Zach said is almost kind of the problem - he's the jokester character who people laugh at, so we're supposed to at worst roll our eyes and dismiss him. It's certainly hard to imagine him suffering any consequences for it, let alone actually apologising. But it's still a slur that's used to taunt, marginalise and dehumanise people, a marker that this humour is not for Chinese people and anyone who's been called that, that it's laughing at them, not with them. From a meta point of view, it's construction and placement seems to be as a punchline, that you're supposed to be laughing with the racism, not even at it. (And the latter is hard at best to pull off that isn't also laughing at the marginalised people.)
Honestly, in my opinion, its inclusion is a mistake. To people who don't care about the racism, it's at best another punchline. To people who might feel alienated by it, it'll make them detract from their enjoyment of the story, may even make them stop reading it, though they'd presumably have a hefty investment by now. To people who enjoy racism... well, do you really want to go after those guys for your audience, especially *this* late into the story? I don't think it's a major thing, but I do think adding it has more downsides than upsides.
Also, I guess, while I'm talking about this kind of thing, the It's a Trap gif someone posted a few pages back made me flinch a little. The meme it draws on, that there's an attractive women who *surprise* has male genitals, is massively transphobic and is a sentiment that not only has got people like me killed - is, honest to god, still getting people like me killed - it's also the defence people have used successfully to walk away from the crime afterwards. It's not a massive thing, which is why I didn't bring it up at the time, and the story itself certainly isn't transphobic, but I thought I'd put it out there.