Ok. I think I know what is going on. Are you using Gmail in Safari or another web browser?
Normally Google detects that you are using a mobile device and re-directs you to the mobile version of their site. It does not have the chat feature. If it ever did, I never noticed. Not that that means much. Google is always changing stuff with little or no notice.
I suppose the actual Gmail app may have also had the chat feature at one time, though again, I never noticed it.
You can force the Desktop version of Gmail in Safari, and it does have the chat and video features. When you have the folder view in the left column, scroll all the way to the bottom. There you will see links t the HTML and Desktop versions of Gmail. Tap the desktop link and you will get the same Gmail site you get on your laptop.
Hold in mind that it may not work perfectly. For instance, scrolling is hit or miss, with the left column pretty much a guaranteed miss.
I recommend you try the Hangout's app and see if it works for you, as I expect it will be a much better experience than the Desktop version of Gmail on the iPad.