Playing movies on Apple TV (4th gen) from external hard drive

I have ripped all the movies I have on my DVDs and Bluerays onto an external hard drive. I did that so that I can watch them using my Apple TV (4th gen). How can I connect this hard drive to the Apple TV? There doesn't seem to be a direct connection. So it looks like I'll have to use a computer that this hard drive would connect to.

I have an iMac (27-inch, Mid 2010) and a Mac mini (Mid 2010) – both don't seem to support AirPlay.

What options do I have to play the movies from that hard drive using the Apple TV?