I took the liberty to produce a proof-of-concept installation
script for the Weird Worlds demo.
The script will download the demo setup executable, a
compatible binary version of wine (0.9.25), and msvcrt.dll.
The script will then proceed to install and configure
everything. The installation is completely local. Just
remove the directory, and it's gone, no system-wide changes
are made.
I should warn you, the script is not very robust, but it
worked flawlessly on several different machines I've tested
it.
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INSTALLATION INSTRUCTIONS:
1.) make an empty directory for the game, for example:
> mkdir ww ; cd ww
2.) get the installation script:
> wget
http://www-f9.ijs.si/~matej/ww/weirdworlds_install.sh
> chmod a+x weirdworlds_install.sh
3.) run the installation script:
> ./weirdworlds_install.sh
Note: when the windows installer starts, install the game in
the default location. Do not run the game or view the Readme
at end of installation (uncheck the boxes).
4.) run the game
> ./weirdworlds_run.sh
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DISCLAIMER:
I hope Shrapnel Games won't mind, since the demo will be
downloaded directly from their site. I also don't know
what is the legal status of the msvcrt.dll, but nowadays
these files are floating around everywhere... Wine should
be ok. 
Cheers,
HMX