I as well, cannot see any of the pictures Doves linked from randomgifs.net
Based on the fact that you can actually see the image when you copy and paste the URL of the image manually into the browser, there is likely a no
hot linking rule attached to that website against certain ISPs.
For example of this, in Firefox, right click where it says Image, then choose 'View Image'. If I'm correct, it will simply redirect you to their homepage. For Chrome, simply right click on the broken image display, then choose 'Open image in new tab'.
Unless if you copy and paste it manually into the browser, there will be no way to view it.