Thin-film electronics would probably be the starting point. As far as I can tell, that industry is very concentrated on display, solar and "gimmick" electronics (think electronic tamper seals or marketing strategies.)
To make this device, you'd need:
- A battery breakthrough (hard)
- Flexible OLED and peripherals (easier)
- Flexible chips (hard but optional)
- High power efficiency or microfluidic cooling (hard depending on thickness.)
Depending on where you let the device be folded, if you had a small enough SoC, you could protect it from bending and hide it in the panel sections that don't have a seam. The trickier bit is raw power and thermals, which will be the bottleneck for the next few years.