BitGym supports mirroring the full screen to Cast capable targets, but does not support an integrated Cast option which only sends the video content.
This is because Google Cast does not support many of the features BitGym needs to operate. For example, it does not support variable speed video playback nor the video overlay and audio effects BitGym makes use of. For this reason it's best to use Chromecast Mirroring or an HDMI cable to mirror your device to a television. Please see our article on viewing BitGym on your TV for more information.