Firpo pushed him through the ropes. That's pretty clear. Also, it just a normal reaction to push away a man who fell on top of you, so the ringside reporters weren't deliberately helping Dempsey up. Curious that the referee broke the two boxers whenever they fought inside.
Yes its edited. Roughly 10 seconds is missing. Round one starts at :52 and ends not at 3:53, but 3:42. Jack time out of the ring is clearly cut. They say 9 seconds, but it looks more like 4-5 on the film. Also Dempsey is technically down at the 2:18 mark as his glove touches the mat preventing him from falling down. Firpo punch resistance looks rather poor, though he did have Dempsey in some trouble in round one.