If you're using your Chromecast and receive a "HTML5 streaming requires Plex Media Server 0.9.8.6 or later" error, there are a few common reasons:
Streaming from a Plex Media Server (Computer)
If you receive the error while trying to stream content from your local Server on your computer or from a Server someone has shared with you, it means that the Server isn't new enough to support what's required for the streaming. The Server will need to be updated to a current version.
Related Page: Plex Downloads
Streaming from a Plex Media Server (NAS)
Some NAS devices–primarily those with processors based on the ARM architecture–have capabilities low enough that transcoding is simply disabled altogether for them in Plex Media Server. You may also see the error message when using these NAS devices where transcoding has been disabled.
Streaming Cloud Sync Content
If you're trying to stream content that's hosted in a Cloud Sync library, you can also receive this error, but it's for a different reason. In this case, it indicates that the Plex App initiating the cast (e.g. the iOS, Android, or Plex Web App) is set such that the streaming video quality settings are lower than what would be required in order to Direct Play the cloud content.
To correct this, you'll just need to adjust the streaming/video quality settings in the casting Plex App preferences so that they're high enough. Often, it's easiest to simply select the highest quality setting just to be sure.