What are they doing actually, crossing through the existing well hole?
Yes that’s the goal. When they intersect the existing bore they will pump mud down to that point and let it begin to come back up the orginal bore towards the surface. They’ll keep increasing the weight of the mud until they reach a point that the length of the mud in the bore plus its weight will stop the flow. Then they can place the cement plug in.
Remember the mud was holding this well until they took it out and replaced it with sea water when they were trying to complete the final process after the first cementing job. That is when the well blew.
Click the following link for a schematic of the operation and estimated depth/location of the relief wells.