If you specifically want an open-world crime game that runs natively on the PPSSPP Emulator, consider these official titles: Grand Theft Auto: Vice City Stories or The Godfather: Mob Wars Scarface: Money. Power. Respect . Kenka Bancho: Badass Rumble (focuses on street brawling and reputation)
Since Sleeping Dogs is not on PSP, the only way to play the actual game on Android is via (since the PS2 version is less demanding than the PS3 version for mobile processors). sleeping dogs ppsspp zip file download for android link
PlayStation 3, PlayStation 4, Xbox 360, and Xbox One. Mac: macOS versions are available. Why You Can't Find a PPSSPP Link If you specifically want an open-world crime game