Is there any PSP game like this?

[Buko Pandan]

The only games I played in PSP with a similar manner of gameplay is Shadow of Destiny (not exactly a visual novel style but it's really good!) and Corpse Party - Book of Shadows, and just like Squall said, most of the games in PSP are Visual Novels (which covers approximately 60% of the total games in the PSP game library) and is only available in Japanese version which makes the selection rather very limited despite of the PSP's huge game library. In my opinion, the Nintendo DS offers a lot more games with puzzler "visual novel game style" of gameplay, here are some titles:

PSP
1. Shadow of Destiny
2. Corpse Party - Book of Shadows


DS Titles
1. 999 - 9 Hours 9 Persons and 9 Doors (the one you played)
2. Trace Memory
3. Time Hollow
4. Phoenix Wright Ace Attorney Series
5. Miles Edgeworth Investigations
6 .Ghost Trick

I'll post some games in PSP with a similar gameplay of your preference when I find some.