Japanese first-person shooters
There are not many of them, so let's try list them all here.
Star Cruiser and Star Cruiser II
A space-sim/FPS hybrid. It has got a cult following in Japan and is almost unknown in the rest of the world. Most of you probably tried the Megadrive port, which is not very good for the following reasons: it's jerky and slow, it has ugly textures, it is linear (you can travel only where the plot allows you), and the economy part is completely cut. The X68000 version is the best IMO. Actual shooter gameplay is as refined as Wolfenstein 3D, it even has strafe controls! The early pre-wolf id software shooters were much much worse.
Iron Angel of the Apocalypse and Iron Angel of the Apocalypse: Return
Wolf 3D style shooter with emphasis on the plot. The first one suffers from choppy framerate and monotonous textures, but the second one is really not bad. It reminds me of Bloodshot from Sega Genesis.
Geograph Seal
Excellent game! FPS with a brilliant jumping technique. Probably the best exclusive X68000 game ever. I wish there was a console port (32X would run this without a problem).
Jumping Flash and Jumping Flash 2
The spiritual successors to Geograph Seal with more platforming elements. Both titles are great, I just wish the developers spent more time on the artwork.
Kileak games
I can't comment on these since I've yet to play them, but the general opinion on the Internet is not very good.
Outtriggers
Not only it's a jFPS, but also an arcade FPS, which is also very rare :) Made by Sega it got a Dreamcast port. Addicting but gets old fast.
Coded Arms
FPS by Konami, haven't tried this either.
Anything else?