I got the demo running on Steam Deck, but there might be something funny with the zip file. The KDE Ark tool would not create a "jre" subfolder, but would extract the files within it with filenames like "jre\bin\java.dll". I got around this issue by using the command line unzip tool. With the files correctly extracted that way, I was able to add SliceAndDice.exe into Steam as a non-Steam game, set it to run with Proton, change the control profile to "mouse only" and then the game seems to be playable.
I hope that helps those who want to play the game on Steam Deck.