Writing at home is irrelevant if what you're doing is related to the company's business. You can't be working for Google and making a browser, a document editor, a spreadsheet, a mapping site, etc... It doesn't matter if you do it on your own time. Yea, you can grow coffee and sell it at retail stores on your own time. No you can't complete directly with your employer. If it's some gray area then you either get permission first or wait for the courts if you get sued.

This isn't unique to Google. It's basic common law. No contract needs to be signed. Competing with your employer is immoral. If you want to compete then quit and be a competitor. If you're taking their money as an employee then you have a "duty of loyalty"