Another feature for the chat window: A refresh button. So no need to hit the URL, again and again, to refresh the chat window along with the whole page.
When you want to see the latest outgoing and /or incoming messages then you can refresh it with the refresh button. The below image gives you the idea.
NOTE:
This option is available in all types of Salesforce Orgs. But if your org supports the streaming APIs then chat window gets refreshed automatically but if it's not then you need to manually refresh it to see the latest messages.
You can use Streaming APIs with any Salesforce Org as long as you enable the API.