But the bulk of the time consuming work is "when user clicks button, track event x," I'm guessing it's a system similar to heap analytics.

I imagine though this only works for uikit applications, and not games as they tend to do all that custom.

Yes, that's true - you have to install the SDK which takes some developer time (though minimal and nearly equivalent to copying and pasting a JS tag)

I'm really trying to stay objective here because I do love me some Mixpanel. However, I'm curious what the response will be to someone with nominal Developer skills who outsourced their app, but sees this as an opportunity to save some money to get data. Seems like a poor experience from a user perspective to get this codeless product going.

We tend to see it as there are many more people in the world who aren't developers that get some valuable data as opposed to guessing or using their gut. For developers, we still have a manual way to do this.