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The gym puzzle would be essentially one of those museum sandboxes where you 'dig for fossils' but scaled up to be the entire interior of the gym. You'd have to fight a trainer whenever you found one, and they would give you clues to where the elevator that takes you to the leader is buried once you defeat them.
This guy is a wannabe Pokemon Professor focusing on fossil pokemon. He's from Hoenn, thus the Nosepass as his partner, and if I was allowed to go all out his full team would basically just be the Hoenn Desert Squad. Outside of the gym, he researches fossil pokemon and 'old' pokemon—see Golurk, Cofagrigus, Bronzong, etc.