The existing switch box is too narrow for my switch
The box is very easy to remove. Just straighten the four tabs and the box will come out, the taps will fall to the floor behind the drywall unless you hold on to them and slide them out from behind the wall in the event you want to reuse the box. 

You could use the existing box once you attach the NM cable to it. Just remember to hold on to those tabs. After making your connections to the switch, wrap two or three wraps of electrical tape around the switch and secure it into the box. 

You can also replace the existing box with a plastic old work box. The box you pictured won't work unless there's a stud right there to drive those screws into.