maybe they're calling it a home console first and foremost because the battery life will be way too short for longer gaming sessions.
Otherwise, yeah it's a handheld. There's nothing new about connecting a mobile device to a TV and using a controller to play games.
It's not been officially supported by Nintendo or Sony in the past but it's
A: possible on hacked handhelds
B: a given on Android devices
C: possible on Windows tablets (even with Nintendo games in combination with emulators)