That didn't take long.
Dutch developer jvanakker hacked the new Apple TV to run a native tvOS web browser. Here's Apple's website on the fourth-generation Apple TV:
Sadly, this app wouldn't be allowed on the tvOS App Store since it uses a private API based on Apple's UIWebView class. The browser, which can be looked at as an interesting proof of concept, lets users scroll through pages with the Siri Remote, with a press on the center of the touch surface bringing up a cursor for clicking.