Hey man I am slightly experienced in the highland games but more so in strongman but I train with a couple of Highlnd Gamers.
They perform alot of Front Squats, Deadlifts, and presses overhead and incline more so than standard flat bench. Also the majority of there pulling workouts and movements are high power movements such as High Pulls, Power Cleans, DB and KB swings ( nothing really closer to weight over bar you can do in most gyms, Pendley Rows, and 100 different variations of the above.
Nothing is more important than a strong as hell core, hips, and grip muscle wise. You need to attack your midsection front, back, left, right, and everything in between.
lastly the absolute most important thing period is technique and practicing with the events them selves. I honest believe this more with Highland Games than any other strength sport. Almost any one can perform most Powerlifts, Oly Lifts, and Strongman events with just small amount of instruction. They may not be the best but good enough that brute strength could when them a meet at a local level. How ever I have seen some stupid strong guys ( myself included not that I’m super strong) get there asses absolutely kicked and embarrassed trying to heave a 40lbs weight over a measly 7-8 ft bar. Same with the caber no mater how strong you are with alot of tech work your going no where. Hope some of that answered something.