In olden times, it was Running Deer, shot at 100 meters with a manually operated centerfire rifle and iron sights. There was a doubles event in which you had to fire two shots per pass. Most shooters concentrated on getting good with a bolt action, but Walter Winans won the Olympic doubles in 1908 with a Rigby double rifle in .22 Savage High Power. The US AMTU built up some heavy barrelled .222 Remington 760 pumps in the 1960s.
But that takes up a lot of room and the range has to handle centerfires, so they watered it down to Running Boar with .22 lr at 50 meters. Scopes came in and slow - fast passes replaced doubles.
But that still calls for actually Shooting a GUN so they cut it back even more and shot reduced targets (Running Piglets?) at 10 meters with air rifles.
But that still calls for shooting at a picture of a Darling Live Animal so now it is shot at a bullseye sliding across the air rifle range. I saw some of the team tryouts for the Olympics and there is just not much going on to see although there is considerable skill required.
There are apparently some of the old deer and boar ranges left around but I doubt anybody is building any new ones. If you want to shoot the event you are going to have to get to one of the remaining facilities. Or start construction.