Does the sound work if you just use the integrated speakers as I believe your computer is a laptop? Are you connecting the headphones before or after starting the launcher and Stellaris? Some games don't notice the default sound output device changing so try to plug them before starting if you were plugging them after.
If you have a custom volume mixer (eg. EarTrumpet from Microsoft's app store or if drivers installed one) which allows you to change volume and mute specific applications I would double check that you haven't accidentally muted launcher or Stellaris.
If the sound works fine in other software and Windows with the previous drivers then I'd say the problem is more likely in Stellaris or in some settings.
These seems to be the latest sound driver from Dell for Alienware 15 R4 so if you tried to install some other drivers which failed to work these might be worth a shot:
https://www.dell.com/support/home/e...code=wt64a&productcode=alienware-15-r4&lwp=rt
Though in most case Windows Update should provide the drivers without issues even if they can be bit older sometimes.