AFAIK it's not possible to stream Mobile Ed courses directly from the Logos computer programme to a TV via Google Chromecast. However, it occurred to me that anyone accessing the Logos web app (http://app.logos.com) can stream directly to Chromecast by using the Google Chrome web browser.
In the computer version, go to http://app.logos.com, find what you want to watch and then, in the Google Chrome browser, click on the menu icon (three vertical dots) and select "cast"; this works not only for Mobile Ed videos but also for whatever is in the web browser. Tip: you can make your video full screen in the Chrome browser and therefore full screen on your TV, but on your computer switch over to the computer version of Logos so that you can read/highlight the text of the transcripts as you hear them delivered on TV.

In the mobile/cell phone version, go to http://app.logos.com, bring up the Mobile Ed video you want to watch and select the cast/stream icon on the bottom right.

Sorry if this workaround is already well known. It only occurred to me and I wanted to share it with others.