With difficulty, if you're a typical end user.
It's important to make a distinction between server generated error pages (e.g. 404 messages or similar), and browser generated pages (e.g. Network problems, server not found). Server generated pages are essentially normal web pages. They can do anything a web page can do, whilst still being an error message which may have been sent with a special error code (such as the common 404) - there is nothing special in the handling of these by browsers, if they provide content. If they don't provide content, browsers will usually give a default message rather than leave the user staring at a blank screen. You generally can't tell the difference between a server generated error page and a browser generated message in this case, unless the server sends an error page which doesn't match your browser - the only difference would be in the size of the response, which an average user may not know how to check.
Browser generated errors are more interesting in this situation. These are shown when the server cannot be contacted for some reason - network failure, mistyped domain name, that sort of thing. In this case, the page shown is generated by the browser. This is key to spotting if it is fake - browser generated content is, effectively, instant to load. It's not coming over the network, so appears as soon as the browser discovers a problem. A fake browser message would have a network delay - might not be much, but it will exist.
You could also open up the built in browser debug tools by pressing F12 and then try refreshing the page. For a genuine network issue, you shouldn't see any traffic being sent or received. For a fake one, there would be at least one connection.
However, is it worth worrying about? What could such a page do? Potentially it could serve up malware, but you wouldn't need to interact with it for that - by the time you notice, it's too late. It can't access any other browser data (cookies and local storage are subject to same origin policy, so are only available to the originating domain), and any flaw that allowed other access would work just as well on a standard page.
In short, you're probably safe to play the dinosaur jumping game on Android Chrome if it pops up!