Installed d3dcompiler_47.dll with protontricks (guide incase anyone hasn't used protontricks before):

1. Open protontricks and select Re:ZERO from the list
2. Click OK on any popups / errors
3. When asked what you want to do, click "Install a Windows DLL or component"
4. Find and select d3dcompiler_47.dll from the list and click OK
5. Click OK on any popups / errors until it asks what you want to do again
6. Play the game (you can close protontricks now)