Just discovered another alternative - if your TV has Android TV built-in, you should be able to install the MFC app on it and watch MFC video content from there.
If it doesn't show up in the Google Play Store, you can side load it by installing an app like Aptoide or Apkpure first. As it's not designed for Android TV you'll need to use a mouse to control it, though.*
At least, it works for the the recorded videos on there, like the highlights, interviews etc - I can't say for sure if it would work for streaming live games as I haven't tried it.
Having just found this myself and started using it yesterday, I'm finding it much more convenient than connecting my laptop via cable, so I'll be using this method from now on.
*Edit - just noticed the OP said he can't use a mouse with his TV, so I guess this wouldn't work for him.