From what I understand on this kind of stuff, it's completely determined by what contracts an employee has signed. "We own everything you do on company property or with company equipment" is basically universal and things done at your job are understood to be works-for-hire, but a company can't just claim "We own everything you do in your free time if it's related to computers" unless the employee has agreed to that in a contact. Am I wrong here?
For your Google example, I would assume their review framework was set up by an agreement with the employees. I had an offer for a job where I was told "Anything you do on your own time is yours. And if you want to put that in a written agreement for a particular project, we're happy to." From what you say, maybe Google doesn't have quite as lax an approach, but their ability to decide what you can and can't work on must have been specified in an employment contract.
They are being generous (or maybe just trying to make sure people don't quit) by signing agreements that let you out of the default law.
1. You're making a competing product.
EA makes games. You're making a game
2. You're have a conflict of interest.
If you figure out how to speed something up 20% at home you arguably have a duty to share that at work. If you have a game idea for your game at home you think it unique you arguably have a duty to share that at work.
It would be up to a judge to decide what "related to their business" means. There's a spectrum. Both are FPS games, One is FPS, one is RTS. One is Online, on is offline. Is a gaming web site related? EA runs a gaming website. I have no idea. Do you want to find out after spending XXX hours on something it belongs to your employer? No? Then maybe you should ask them.
Note: Many companies will sign an agreement on request and review that allow you to make things that might have a conflict of interest. My understanding is EA specifically does this because so many of their employees wanted to make mobile games on the side. I have no idea what that agreement says. It might say EA gets the first right to publish it. Again I have no idea.
I know Google allows outside projects with permission. You submit a description of your project. They review it. If they don't see a conflict of interest they'll give you a signed document saying so so you can work on it with no issues.