I have been trying to figure this same thing myself, but I haven't been able to find anything that allows you to download the pictures from their website onto your PC directly.
However, if you're on PS4, you can open the Snapshots menu ingame -> open the snapshot you want to have on your PC -> hide the HUD by pressing X and then take a picture of it using the Share button on the PS4 controller. Then after that, plug a USB memory stick on to the console, go to Capture Gallery and transfer the picture you took onto the memory stick, from there just plug the stick in to your PC and you have the picture(s) there for you to upload to social media or whatever you wanna do with it. Of course this isn't the best solution, but at the moment it seems to be the only way of getting pics from the game onto your PC...
Also, on Xbox One, I think there is a way, but I'm not exactly sure how to do it as I'm not playing on that console but, I have seen a few people post links to a website called "account.xbox.com/screenshot" and then the rest of the URL for the picture. No idea about the exact way of getting pictures there, but it might be worth checking out if you're on that console