"~/.wine is not owned by you", am I safe?

Wine expects that $WINEPREFIX (which defaults to ~/.wine) be owned by you. When you run wine with sudo, ~/.wine is owned by you, but wine is running as root. Hence the error. Wine immediately quits when this happens, so you don't need to worry, no damage was done.

You don't need to reset ownerships as in Zanna's answer (this particular run of wine didn't make any changes), but that's usually harmless.

Note that Wine applications have as much access to the system as the user they run as, so running Wine as root, as you have realised, is dangerous.

Nothing too terrible has happened ;) root might have become owner of the wine config directory, that's all.

You can fix any potential issues by making sure you are the owner of that directory. When logged in on your normal user account, run (typing very carefully):

sudo chown -R $USER: ~/.wine