The embed.twitch.tv link will show the chat beside the player if there is plenty of space on the screen. If you try to minimize the width of the embed it will show the chat below the player.
Example:
Before
<iframe src="https://embed.twitch.tv/?channel=lirik" width="1200" height="600"></iframe>
Preview: imgur.com
After
<iframe src="https://embed.twitch.tv/?channel=lirik" width="400" height="600"></iframe>
Preview: imgur.com
