I don't think I've ever seen a video of him using kettlebells, just that picture where he stands next to them that everyone speculated about.
More recently I've seen him use weights, but he said for many years he never used...during Pride, etc. Videos showed him running, pull-ups, push-ups, planks, band exercises, using a sledgehammer.
As for training in Russia in general, Aaron Pico has trained with the Russian national team recently and said presently they don't lift weights. Mostly, they just wrestle.
I have some friends who went pretty far in the sport, they said there is a pretty big contrast between USA training and there.
USA is a lot of machismo, working guys out till they feel like dropping dead, Russia treats it more like an art form, mastering the technique.