Retro gaming is a massively popular Raspberry Pi application, and while loading your favourite old video games onto an SD card is pretty straightforward, building the physical shell of a gaming system can be daunting for those of us without 3D printers or design skills of any kind. PiBoy Mini bridges that gap by providing partially-assembled devices to their customers. The rest is BYORP: bring your own Raspberry Pi.
I don’t see how that could be a PiBoy issue (except for the fan, but that could be caused by high CPU usage).
Slow bootup could be an issue with the RPi or the microSD card, or most likely the OS that you chose run on it.