Yes, you are able to record a second monitor with Screencastify with a desktop recording.
- Open the extension's Recording Control Panel
- Click the "DESKTOP" option
- Choose your audio and video settings
- Click "RECORD DESKTOP"
- A window will appear and ask you which screen you'd like to record. In the Your Entire Screen tab, select the screen of the monitor you wish to record.
Once you begin a desktop recording on a particular monitor, you won't be able to switch the focus to your other monitor in the same recording.