Hi LadyLep,
Yes, you can use your CatheLive/Cathe OnDemand subscription on an Xbox. Internet Explorer is pre-installed on the Xbox One, but if you have an Xbox 360, make sure you have Internet Explorer installed on your device (instructions are here if you don't:
Internet Explorer on Xbox Live | Xbox Internet Explorer). You can navigate to Cathe's website and log in as normal!
If you want to play videos through your computer, you can also add an Apple TV to your television and use AirPlay to mirror your Mac's screen. Information for doing this can be found here:
About AirPlay Mirroring in OS X