I can add some important information that might save you some headaches that the fellow in the video had no way of knowing. If you stop the video right about 3:09 you'll notice the small hand isn't on either side of the zero. This in and of itself isn't terrible but it tells me he didn't pre-wind the mainspring tension before reassembly and his indicator will absolutely not be accurate in one direction.
99% of the time the shock from a dropped indicator will either damage the rack and or pinnion gear (rare) or merely pull the main gear (sometimes referred to as a pinnion) away from the rack so that the main spring tension is released. When you repair your indicator it is important to look carefully at the gear contact points. If you see damage as shown below, replace the damaged part.
Assuming you were lucky and there is no damage check the action of the stem to see if it moves freely inside the body. It is almost impossible to bend a stem because they are very hard, but the plunger tube the stem passes through can become disoriented inside the indicator body and may need realigned. It's not as scientific as it sounds.
The indicator shown in the video did not require the hands to be removed before getting to the screws under the face. I have never been so lucky in all the years I've been repairing gauges. You can buy a cheap hand puller on Ebay for $5. Of course you can try to remove them another way, just don't bend the stem!
Before reassembling the face you have to pre-wind the main spring. This is done before you put the face back onto the body by rotating the big hand while you watch the mainspring coil to see that it is getting smaller with each revolution. If it's getting larger in diameter you're turning the wrong way. On a test indicator I give it about 6 revolutions. On a dial indicator it will always be a lot more. In the video he should have rotated the big hand to tighten the main spring until the small hand was approaching the zero and the big hand was about .04" away from zero. (I'm assuming the hands were still timed) You want the hands to coincide so that they both are at zero at the same time. It's easier to do if you took the hands off first.
Once you have the spring tensioned keep your finger on the big hand to hold the spring in the wound state while you reassemble the face to the body and get the rack and pinion meshed. Put some screws in snug and work the stem and listen to the gears. If they are noisy, loosen the screws and move the face slightly until they quiet down then tighten them and reassemble the indicator.
I test my repaired indicators on a special calibration fixture called an "Indi-check" through out the range both forwards and backwards to verify that all the problems were found and corrected. Dropped gauges do the darnedest things sometimes.