One of the fields where vintage palmtops can easily compete with modern gadgets, is adventure gaming. I mean those games where you type "examine box" and the computer tells you that there is a small piece of paper inside. Or something else. A lot of games were written for portable computers in the heyday of adventure gaming (80's and the beginning of 90's).
Yes, there are adventures for the Organiser. You may download a port of Colossal Cave Adventure and an original game "City of Alzan" from The Psion Organiser II site. They should run on an CM! (haven't tested though)
Psion Series (SIBO)
Psion Series (EPOC)
For Psion 5 (and higher) there is FrotzS5 Z-Code interpreter. This lets you play hundreds of games stored on Interactive Fiction Archive website and elsewhere on the Internet. You may also want to take a look at this page, where you can find a brief installation info together with an entire Zork trilogy for download. (Here's an archived instruction manual for FrotzS5.)
There are a few amusing adventure games available from Tim's Amstrad NC Users' Site, like "Crystal of Nebumeth". NC's full-sized keyboard and large screen make it really comfortable to play adventures even for a long time. Amstrad has a BBC BASIC interpreter built in, so new games may be easily written (the source codes of existing games may help you get started).
You can download a few games from atari-portfolio.co.uk. I don't think that any DOS Z-code interpreter would run on a Portfolio, but I didn't even try. Maybe there is a lightweight version, capable of running on a very basic XT?
EDIT: There is an interpreter with a few games (including Zork Trilogy). You can download it from PofoWiki's download section (infocom.zip).
There are some titles on the S.U.P.E.R. site. You need to be patient, though, and click through those hundreds of programs listed (no categories). DZip (16-bit DOS version) should run on every LX (most likely on 200LX).
There are a few Z-code interpreters for Palms, like Pilot Frotz or Pilot Zip, but I've used only one of them - Frobnitz. It supports all Z-code file formats (except V6) and is quite powerful, but larger games are slow like hell on my IIIe.