Hmmm, that's odd. I have the Attach files button here, even in PMs. (Safari on Mac ... which is usually the worst at behaving properly!) From your screencap, though, it sho nuff isn't there for you.
This sounds like a Xenforo bug, since we don't have any control over things like that. (It's not a setting.) So I'm guessing you would have the same issue on VI-Control?
There are a couple workaround possibilities. The first is to just drag-n-drop an image into the message. That's what I do in posts anyway (rather than clicking the Attach Files button), since it's quicker, plus easier to place where the image goes.
You can also use Command-P (on Mac) which pops up a Drag Image box. That's also accessible with the Image button just to the right of the smilie button in your picture. (With those top buttons, Insert Image is possible, but Insert Media or Insert Video are not.)