I didn't notice this small corner before, but it is small, so I have no idea when it started. It resembles the corner of a piece of paper when we fold it.
This is a screenshot of how it looks like:
Removing the other code, the corner appears like this:
The remaining code is an iframe, with this code (ellipses indicate more code):
<iframe src="https://hangouts.google.com/webchat/load?prop=gmail(...)" (...) id="gtn-roster-iframe-id"></iframe>
Since Hangouts are mentioned, and I'm still using the old chat in this account, I decided to check my second account, in which I have Hangouts enabled:
Does anyone know why this happens? Does it have any purpose? Will it ever change, after some action? Is the page tearing, because of how old the chat is?!
Additional info: I am using Firefox in Mac, and this happens even in Private Browsing. I tried with Safari, and the same corner appears in Private Browsing as well. Using Safari's User Agent "Switcher", the behaviour is the same in every available browser (also in Private Browsing). I don't have extensions or plug-ins in any of the browsers. I also installed Chrome, and the same happened even in Incognito Mode.
Update: The linked page now states that
Google Chat was officially shut down on June 26, 2017.
I was now forced to Hangouts, which made the "corner" disappear.
Best Answer
It seems to be a not-very-well-hidden iframe for the old-style Gmail chat. Considering how old the old Gmail chat is, and that you're not seeing it with the more modern (but now still possibly outdated) Hangouts, it just seems like a bit of forgotten code that wasn't as well-crafted as the usual Google code we see.
I don't think it is anything special.