A good way to think of strongman training is a combination of factors which include Crossfit and Powerlifting.
Strongmen have a focus on absolute strength, however they are functional athletes that have to cover many disciplines. There is less variety to their events compared with a crossfit athlete, which means they are able to focus on training specific lifts / events more frequently.
While most strongmen are not concerned about keeping their weight down, they generally look to build muscle size (hypertrophy) as well as absolute strength thanks to CNS stimulation.
Many strongman events do have a large cardiovascular factor, which is why strongmen must ensure they have adequate aerobic capacity and that these attributes are training regularly.