Heck, even if the authentication step was 100% secure, what's stopping a malicious user from calling increase("farms") on a previously authenticated Fukime object? The Fukime instance is shown to have direct access to "global" variables, so the user wouldn't be limited to screwing with their own data.
This kind of logic belongs server-side (and this obviously isn't a server-side API, because the examples provided are for Android and iOS.)
If someone wants to misrepresent how many times they've installed your app, there's nothing you can do about it. (They could just uninstall then reinstall over and over.)
Though... obviously they should only be able to mess with their own statistics, not the global statistics.
That way, if the user was to do stupid things to their own variables, they could just be removed when calculating the global ones.