The "less clickable space" doesn't matter here, since it's on the edge of the screen and the user has "virtual" space to click.
From "Designing mobile interfaces" (O'reilly, 2008):
Buttons at the edges of screens with flat bezels may take advantage of this to use smaller target sizes. The user may place her finger so that part of the touch is on the bezel (off the sensing area of the screen). This will effectively reduce the size of her finger, and allow smaller input areas.
Google maps (for android) does it, so that the space is saved for the important content: the map.
Compare also to Nielsen's "Mobile Usabilty":
consider ways of temporarily hiding parts of the chrome and reveal it only when needed
If google could they would've hidden the button completely. But since that doesnt work, because you need an easy and discoverable way to show the menu/controls the probably decided on this "compromise"
I also don't think that it looks broken - on the contrary, it invites you to click it.