This looks like an old copy of the demo. You can find the latest version here:
https://javascript.daypilot.org/demo/scheduler/eventmenu.html
It should work fine for both the time range selection (use right mouse button to make the selection) and events.
The latest version seems to have a bug that doesn't allow you to invoke the context menu on the existing time range selection. That is fixed in the latest sandbox build (2021.3.5045):
https://javascript.daypilot.org/sandbox/scheduler/eventmenu.html
Please let me know if the problem persists.