Considering that button says I'm not logged into patreon, I don't have internet on a laptop (that I copied the game to) when I play it, and all I do is hit play, I'd say their check is not working.Early last year the developers implemented increasing levels of patreon-related security checks. While the game originally validated nothing and could just be run post-download, now it actually looks for subscriber-specific information dumped into appdata by the launcher upon login, and without that information will leave you with a fancy screen informing you (in broken English) that you are not a subscriber.
This means that, barring a crack to remove the Patreon check, functional downloads of Patreon-specific versions are guaranteed to get the account that leaked them banned. Not many people are willing to make a new throwaway account twice a month (And spend $30 monthly in the process!) just to keep a single game up to date on this forum.
There may be some subscriber related data in appdatta, but that's not where the check really is, it's in the registry data. I know this since I tried copying just the game and appdatta and it wouldn't work without me logging in until I checked and copied all the registry data to the laptop.
Maybe my Patreon launcher from the December release is different somehow. Who knows.