This picture is a nice illustration of why it is so dangerous to work on oil rigs. You can see that there are many places to smash your hands and fingers, many things that can fall on you, and many things you can fall off of. Basically a lot of very big parts moving in lots of directions all around you.
As far as what is happening in the picture . . . my best guess is that they are Coming Out of the Hole here. Periodically, the drill bit has to be changed. The drill bit, of course, is at the bottom of the hole, so they have to remove each piece of 30 ft drill stem one at a time. I believe that is what they are doing here. Someone who was worked on rigs more than me can probably say with more certainty what they are doing.