If you're looking for alternative racing games on PSP, there are several great options available, including Burnout Legends, Wipeout Pure, and Gran Turismo PSP. While these games may not be as iconic as Mario Kart, they offer exciting gameplay and fun racing experiences.

Moreover, the PSP console is not compatible with Nintendo games, and it's not possible to install or play Mario Kart 8 Deluxe on PSP using any method. The game's system requirements and compatibility are specifically designed for Nintendo consoles, making it impossible to run on PSP.

In conclusion, it's not possible to download Mario Kart 8 Deluxe on PSP due to console exclusivity, system requirements, and licensing restrictions. However, you can play the game on Nintendo Switch or other Nintendo consoles.