Goto Steam -> Settings -> Game Recording.

Scroll all the way down, and look for "Audio Recording" Section. Next to "Record Audio from..." choose "All System Audio". If you only want your game audio, then choose "Game and Selected Programs" then under the select additional programs choose your game .exe.

Some games (like elite dangerous) don't record their audios due to how the game devs programmed it (I'm not sure, but it has to do with steam locating the audio of the game, and the game itself is not using the default location).