Yah the bike in the image has disk brakes. you can see the disk at the centre of the wheel. Disk brakes have "handlebar" brake levers, but the braking force is directed by small pads that grind against a disk - just like car brakes. They can be mechanical or hydraulic based.
By hand brakes, you mean rim brakes. Disc brakes are operated by hand, and they work. The only brake I can think of that's not a hand brake is a coaster brake.
The pictures are a bit blurry and I'm not up to date on my hipster brake technology, but he seems to have hand brakes. With enough clearance, this shouldn't be a big problem.