Thousands of people playing your 404 Flash game (and using server resources) isn't what you want when you can barely keep your core service alive. Also, it would provide yet another thing for Twitter users to complain about.

Why would flash games use "server resources?" It's just bandwidth, which has never been Twitter's problem.

Besides, you can embed it from an external site or CDN.

While on the side topic of maintenance (rather than 404) pages, digg's got the most useful one I've ever seen:

http://flickr.com/photos/alabut/2947148797/