Of course, it does. There is a problem on your system. What happens when you click it?
If nothing happens, go to Applications > Adobe InDesign CC 2015 [assuming you're running the latest version] > Adobe InDesign CC 2015.app, right-click and choose Open. Once open right-click on the Dock icon and choose Options > Keep in Dock.
If it still doesn't open, uninstall (from the CC app) and install again.
But the fact that you're also having a problem with Illustrator could point to deeper system problems.
Thanks for the quick reply. It's actually a relief to hear this isn't being done on purpose by Adobe. :+) After experiencing this frustrating issue and submitting my original post, now all CC apps open as they should. This is VERY strange and unsettling.
When attempting to run either of these apps from the dock or from the apps themselves, I got an error simply saying the app couldn't be opened. I can't get the error now or take a screenshot of it, because everything is strangely back to normal.
Sounds like you need a Ghostbuster!
I do keep a very clean system, and employ anti-virus, etc. I suspect it had something to do with the Creative Cloud app/monitoring system being in some kind of transition state.
It did scare me though, like a good ghost should. :+)