Arcadia slider door parts

The part you're referring to is the keeper. Or at least, they are normally; truth be told, I don't know what the exact style is called on your door. It looks like it's just a screw sticking out of the frame.

All's well, though, because the 82-005 comes with its own keeper that is specifically designed to work with it. The only catch is that you will need to find a way to retrofit it on your door, which could be easy or difficult depending on the frame. In my experience, the older a door is the more creative I have to get with finding out the best way to mount the keeper. 

To assist in this, it comes with a bracket that allows it to mount at a 90 degree angle, if necessary. Just don't expect it to be immediately obvious where the keeper needs to install. The trick is to hold the handle up to a closed door about where it would install and note where the hook latch comes to rest. You would then install the hardware appropriately.

Looking at your first photo, I see a pretty significant portion of the door frame that would give you enough room to install a keeper. It's right where the handle butts up while the door is closed. Is there any reason why you can't use that area?