It has a massive heatsink inside of it, it's passively cooled but it's a big chunk of metal the size of the keyboard, which is more than enough for this chip.
There is a heatsink. It's a large chunk of metal under the keyboard.
I personally think this product looks awesome, maybe partly nostalgia.
It does, but it would hardly look worse if it were wider. It would break no canon either - e.g. Amiga had the same form-factor but with a full-size keyboard incl. keypad.