What game did that come out of?
It's easy to tell if the cap is factory or not. Let's see a close up shot of the soldering on the other side of that board (or any other one with a failed cap), to see if it's the original factory wave soldering.
Also, let's see a pic of the full details of the cap (size, etc).
And let's see a pic showing measurements on those four original diodes in the upper right corner. Because the main failure mode of AR's of that age are those 1A diodes, not the caps. That's why Atari upgraded them to larger diodes on the later versions.