Any website or video claiming to offer a "Mario Kart 8 Deluxe PSP download" is . These typically contain malware, viruses, or misleading ads. There is no legitimate PSP version of the game.
If you have a custom firmware (CFW) PSP, you can install an N64 emulator like DaedalusX64 . You can then run a ROM of: mario kart 8 deluxe psp download new