Yeah, as long as there is a way to cast video to the device I think it works...some consumers may struggle with that as they are used to apps being on device, but it works for me.
The battery issue, I agree it is kind of a single room device, but I could see wanting to move it around the room I am in. If I am say, washing dishes versus cooking at the stove, versus doing prep work. Right now I move an iPad around with me in the kitchen. Also, for when there is a facetime call being able to best position it for what I am currently doing verus having to move to the device and face it.
Unless made for a square display, video will not be ideal on this device. Even SD NTSC content is 4:3 and would require cropping or matting. Anything modern would be tiny on this display.
I think the aspect ratio makes sense for the form factor, recipes, FaceTime, music, etc. but it won’t be a very good video device.