Unable to do a partial screen recording on OSX with quicktime
You can record a selected area of your screen as follows:


Open the Quicktime Player app
Choose File -> New Screen Recording or CtrlCommandN
Now select the area you want to record
Press the button in the middle of you selected area that states: Start recording
To stop, there will be a squared stop button that appears in the menu bar


As your screenshot is missing this button, you might want te restart Quicktime Player or reboot your machine.