Okay, I went ahead and tried this out.
- Installed Linux Mint
- Ran suggested updates by the OS
- Downloaded and opened Stencyl (extract .tar.gz, double-click the "Stencyl" file, select "Run")
At this point, I was able to test both Flash and HTML5 games in Stencyl. Perhaps this is enough for your use of Stencyl in the classroom. If it is, you don't need to do anything more. If you want to unlock more of the targets, you'll need to install some components through the terminal.
To test on Native Linux, Cppia, and Android, you need to install the c++ development packages, same as written in the guide.
sudo apt-get install g++ libgc-dev libxext-dev
To publish HTML5 games, and to test on Android, you also need the JDK. I followed the first link I sent you step by step, and it worked fine, so you can probably ignore the second link I posted.
(Note: You can pick whatever version of the jdk you want. 8, 11, and 13 should all work fine.)
wget -qO - https://adoptopenjdk.jfrog.io/adoptopenjdk/api/gpg/key/public | sudo apt-key add -
sudo add-apt-repository --yes https://adoptopenjdk.jfrog.io/adoptopenjdk/deb/
sudo apt-get update
sudo apt-get install adoptopenjdk-11-hotspot
Set the path to the JDK at File > Preferences > Tools > JDK to the following:
/usr/lib/jvm/adoptopenjdk-11-hotspot-amd64
You can probably ignore all of the 32-bit support packages the guide mentioned. That is, everything in steps 2 and 3.