Fate/EXTRA is an RPG written by Kinoko Nasu of Type-Moon fame, and indeed this does take place in the framilier world of Type-Moon, or the "Nasuverse" as fans call it, but their is a catch. This game takes place in an "Alternate Universe", a world that split off from the "Main" Nasuverse" in the year 1980.
The world is set in a school called Tsukumihara Academy, a fictional place existing with an artificial environment called the Moon Cell. There, the Moon Cell orchestrates a replication of the Holy Grail War using a system called Serial Phantasm or SE.RA.PH, which handles the summoning of Servants. Servant data is taken from the Automaton, a spiritual computer system built on the lunar surface by a pre-human civilization and discovered by humans in the year 2032. The Automaton has monitored and recorded all occurrences on the Earth (including the activities of human heroes) since time immemorial.
Each of the 128 participants in the war must duel the other Masters in a place called the Arena, where failure results in deletion from both the real and digital worlds. When only one remains, the "Holy Grail" shall grant the victor's wish.
Fate/EXTRA is rather similer to ATLUS' Persona series (more accurately, P3P and P4) in that it's an RPG that is divided into two halves, a "school life" section and a "Dungeon Crawling" section that you can choose to do at anytime. At the beginning you also have the option to choose your characters gender which will differate the two gender's stories in small ways, you can also choose which of 3 Servants you want to be your partner. Their Saber (considered "Easy Mode")
Combat is divided into something like a Rock>Paper>Scicors Element but of course their's still plenty of elements of strategy in it since if you don't carefully plan out your moves you won't make it very far. Here's a few videos of the game in action http://www.youtube.com/watch?v=DDpzbzHabas
I believe that Askys should look into bringing this over because it's a nice and fun RPG for the PSP that has a very engaging storyline. The anime and manga adaptations of the Visual Novel have been brought over, along with the fighting game Fate/Unlimited Codes and have sold well so I believe there's definitely an interested fanbase here that would love to see this brought over.
Theirs of course more people wanting to see this brought over on the ATLUS and NISA forums
The official site for the game can be found here, along with two mini games involving Saber and Caster!