Duh: don’t start the Chromecast extension in Google Chrome, but run Chromecast.app on your Macbook (:
To change the WiFi network your Chromecast is connected to, simply open up the Chromecast app on your phone, tablet, or computer and select your Chromecast from the list. From the Chromecast settings page, select your current Wi-Fi network name and select a new network from the drop-down list.
–jeroen