The author is intentionally limiting this app to touch-only for touch-capable users. This breaks the game for anyone wanting to use a touchpad or mouse on their touchscreen laptop.
We actually changed this recently in Stripe Checkout. Touch detection worked great for 99% of cases, but serving a touch-only experience to devices like yours was pretty clearly unacceptable.
We're now treating the touch-only versions as optimized for specific platforms. For example, we have a mobile version that is optimized for, and only displays on, Android and iOS. Going forward, we may explore a pointer event polyfill to improve support for less common touch devices.
Further more it is completely unusable on some touch devices, I tried iPad 4 and iPhone 5. They both scroll the page (better: bump to the top, as if you wanted to scroll past the end of a page) instead of moving the blocks. :-/
The offending code (from http://gameaboutsquares.com/game.c.js, beautified):
Never do this! Remove the entire try-catch block. There is absolutely no reason for you to be limiting touch-capable users to touch-only.