Google chat video may be archived depending on the conversation context. Google does not archive personal video calls made through the Gmail client or Google+ Hangouts. However, Google records and archives video from Hangouts On Air conversations for future sharing over YouTube. Hangouts On Air is a public live stream of a chat that anyone can view; Hangouts On Air are often used for things like community Q&A sessions as opposed to private conversations.
What Gets Archived
Google Hangouts handles both On Air and private conversations and won't work without installing a plug-in. You can launch "1:1" and Hangout chats through Gmail Google Talk which keeps a running, searchable archive of text from conversations. Gmail chat has an option that preemptively excludes chat text content from the archive called "Off the Record." Off the Record mode can be activated by clicking on the "More" option on the chat window and selecting "Go off the Record." Gmail chat will record if you made a video call in the chat history, but it will not record the contents of the video chat unless the chat is configured as a Hangout On Air.
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