In short, no, it is not possible.
In addition to having a smaller screen, the Makerbuino simply doesn’t have enough ram: if you want to emulate gameboy/nes games on the makerbuino, it just can’t be done. (In theory it might be able to emulate the games, but not even close to playable speeds, and the code to do so would be complex and hard to port. Imagine an immensely complex program to run a gameboy game at half a frame per second, but the screen can’t even display it correctly.)
Also, if you were wanting to actually port commercial gameboy or nes games, that is also not possible. All that is available for those games is assembly code. Porting the assembly would be impossible for a beginner, and even someone with experience would not attempt it. Believe me, this is not something you would want to try. So much would have to be changed that it would be far easier to write it from scratch.
For open-source homebrew games written in C, the logic could perhaps be ported, but many features would likely need to be cut, and they again wouldn’t be designed for the smaller screen. I don’t recommend this.
I recommend taking the games you would like to see on the Makerbuino as inspiration and creating a new game inspired by those games.