Yes—that is hot glue, holding the home button bracket to the front panel. Good luck transferring that to your replacement glass. (Which you're going to have to do, to keep the Touch ID functionality after a cracked screen repair.)

Looks like the cable is a bit of a nightmare all by itself.

Apple's system for implementing Touch ID seems to require launching about a year before it's ready. Remember the Touch ID cable in the iPhone 5s? And the much-improved placement in the iPhone 6?

No surprises here: Touch ID in the Mini is powered by an NXP Semiconductors 8416A1 Touch ID Sensor.