Unable to brew install wine

Good work with the detailed error message. I would try to install just libpng with brew install libpng and then if that fails brew update && brew update && brew doctor just to check out common issues. ( I know you said you tried this - but it's not clear that you succeeded with that try)

The above recommendation is from https://github.com/Homebrew/brew/blob/master/docs/README.md#readme

That links to the Troubleshooting Checklist for if you find one package that fails you (looks like libpng from your logs so far).

run brew gist-logs <formula> (where <formula> is the name of the formula that fails you).