The speech recognition APIs that you're referring to are indeed new and not fully supported.
They are also not official HTML5 APIs -- they are currently marked as unofficial. That doesn't mean they won't eventually become official APIs, but for now they are just something that Google thought would be a good idea.
You can find info about them on the CanIUse website. As you'll see on this page, they are supported in Chrome and Opera, and also in Firefox, although only as an experimental feature, meaning that the user would have to enable the feature manually in the browser.
More significantly in relation to your question, the page also states that they are "In development" for Microsoft Edge. This means that there is a good chance that they'll be available in Edge in a future release, within a reasonable space of time. They are not available now, and will never be available in IE, as Microsoft are only developing new features for Edge now.
Therefore, if you need to support IE, you will need something else. There is nothing standard or even well-known that I can recommend though.