The other realistic way to distribute stuff is platform specific installers. It doesn't hurt and it's not complete rocket science, although I confess that I've got no idea how to make something that installs on Linux reliably. If I did, I would be embedding a hacked VM in it which might make life easier.
Cas

Simply double-clicking the jar file in Linux can do the job. Otherwise, a SH file is just like a BAT file in Windows. Most of the time, right-clicking the item to run and accessing its Properties will have a tab at the top that says "Permissions." An item there should say something to the effect of "Allow executing as a program." If checked, then all should be good to go for double-clicking.
If you follow some basic rules it's really not hard to have webstart/applet/exe versions of your game all running from the same identical code, so there's very little excuse IMHO. Webstart is good for easy deployment for java-savy developers like around here, but for your average windows user it blows hard.
Is that because so much clicking is required just to run a Web Start software? I noticed a few issues with the executable. For multi-clicking, I figure a statement to participants might suffice.