i was told an advantage of Linux is if a task hangs others will continue running
This is correct, most of the time. The fact that you could switch desktops, and move the cursor the entire system was not hung.
What happened is hard to say. Some programs are not well written. I don't use Dosbox, so no comment there.
If it happens again, look under System --> Admin --> System monitor. There is a Process tab. That will show the status of all running processes on the system. It may give you a clew if you have a process not responding, or some strange state. You can Kill the process to see if that gets things going again.
System logs are another place to look for errors. You may not know what you are looking for, sometimes it may give you some help. Remember what hung may not be hung, just waiting for a response from some outside resource, ie a network response.
Any way, it wasn't the Blue Screen of Death...
Hope this helps.