But after looking at the actual footage on youtube, everything shot with this camera looks like video
You can make almost any camera look like "video", but alternatively you can make almost any camera look more "filmic" ( I really hate this term ) with controlled lighting and the right post processing.
...I haven't checked these videos for "filmic-ness", but you will likely find something close to what you are after among the 805 GH4 videos in the Vimeo GH4 Group