The main advantage for Quake 3 was that the server, client and UI code could be compiled into platform-independent bytecode modules. This was mostly a boon to mod creators, who had to build only one version of their mod that would work on all Windows, Mac and Linux systems alike.
I thought I heard this was also a boon for the scenario creators and level builders working alongside the graphics engineeers.
They get something a little less hairy and volatile to work with, and execution speed isn’t that critical because you’re only making hundreds or thousands of decisions per second.
Speculation: Assuming the VM has no bugs it is sandboxed. The code run can't access the file system or freely allocate memory. Thus code from less trusted sources can be executed. (Another comment indicates that the VM has a history of bugs, so it might not be advisable, but I have no experience with it)