Apple dictation missing commands in web browser
Google docs uses a custom javascript application that disables the services component of the Mac (that lets the built in Mac voice dictation work.). If you want to use voice dictation in Google Docs, you have to use there build in functionally, and you MUST use Google Chrome.

From Google:


  For an easy way to put words on a page, you can type with your voice in a document. At the moment, this feature is only available in Chrome
  browsers.


Here's how to activate the type with your voice function for Google Docs.


In a Chrome browser, open a Google Docs document.
Click the Tools menu -&gt; Voice typing...

A pop-up microphone box will appear. When you are ready to speak your text, click the microphone or press Cmd + Shift + S on your keyboard.

If this is the first time you've let Chrome use your microphone you will get a little pop-up from the top of the screen asking to OK Chrome using your microphone. Hit Allow to enable the microphone in Chrome.

Once you click in the Click to Speak box, the mic icon will turn orange and appear in a circle.

You can now dictate into your Google Docs. As you do the mic icon will show when it detects sound with an outer ring.

When you're finished, click the microphone again.


From Google:


  While voice typing in Google Docs is only available on computers, many Android and iOS phones and tablets have built-in microphones that
  you can use with a document. Look for the microphone icon on your
  mobile keyboard.


For more information you can check out the Google Help Documentation here:
Typing With Your Voice.