What is the ruling on DS games that are downloaded from the internet in "ROM" format and played via a small device, given that original copies are not available locally and their price is high (100 riyals)?

It is not permissible to play electronic games unless they are free from Sharia prohibitions and do not distract one from an obligation. Excessive playing of them compromises integrity (muru'ah) and wastes time. If the games are free or their owners have given permission for them, there is no problem. However, if they are copyrighted and downloading them is prohibited except for a fee, then it is not permissible to copy or download them without the owners' permission.