ituneskeyboardmusic
Given the age of this question, and the fact that it's about the remote, I think there's merit in asking this again, and separately:
On a Mac keyboard the F8 key is also a play/pause button. By default, it controls iTunes. I would like to use it to control another program (specifically Vox)
The software Beardedspice provides a user-friendly approach to prioritizing Spotify for your media keys. It runs in the background and gives you a few simple settings in the Mac menu bar. It just works.
Download and installation
It can be downloaded and installed directly from the Beardedspice homepage, or by using e.g. Homebrew:
brew install --cask beardedspice
Notes
Update 2021-01-16 - Use Beardedspice as the alternative app Mac Media Key Forwarder is no longer being updated
As there are reports of Mac Media Key Forwarder not working for some users, and the developer no longer updating the app, it is recommended to use Beardedspice.
Nevertheless, Mac Media Key Forwarder will still work fine for most people running on e.g. MacOS High Sierra, Mojave, Catalina, or Big Sur so it remains an alternative.
Download and installation
It can be downloaded and installed directly from GitHub, or by using e.g. Homebrew:
brew install --cask macmediakeyforwarder
It appears that there is a Gist on GitHub using USB Overdrive and a Windows Keyboard that addresses how to map the media keys the way you want to. Configure media keys on a non-Apple keyboard to control Spotify via AppleScript and USB Overdrive on OSX.
If you scroll down to ludalex addition to the Gist, they have added an Applescript that can identify either iTunes or Spotify and assign the Play/Pause key press to the correct app.
Best Answer
It's possible, but not without third-party software or scripting.
You can use the Vox preference pane to set this though:
(go to Vox → Preferences → Controls → Setup)