The initial description of this issue is incorrect. It's not a minimize/restore problem. A more accurate description would be "Closed Opera Dock icon won't open a new window or new tab."
There's something about the old Dock icon that isn't working. Remove and re-add it.
- Close Opera.
- Right-click on the Opera icon in the Dock and under Options, Remove from Dock.
- Use Spotlight to run Opera.
- Right-click on the Opera icon in the Dock and under Options, Keep in Dock.
I'm not sure what changed, but removing and re-adding the icon fixed it for me.