A small Powerbank could help in that case, if no power socket is available. But generally power sockets aren't far away from HDMI ports, at least in my experience.
This exists but is a lot of money for a bad computer. By comparison an intel NUC can actually be a decent computer at 4.6 x 4.41 x 2.01 inches. Why would you actually want this?
I'm waiting for the PC that's the size of a thumb drive that you just put into any hdmi port.
All peripherals connect over bluetooth, and power will have to come from the hdmi port.