Flight Instructor reported a gear-up landing while conducting a flight review in an unfamiliar aircraft at an unfamiliar location.

Narrative

I was contacted by a pilot [who] needed a Flight Review by the end of [the month]. He owns 2 aircraft. We were going to fly his Aircraft X. I arrived around XAam and we conducted a ground discussion. We agreed on what type of air work he wanted to do. The plan was for slow flight; ground reference and short; soft and crosswind operations. His medical is current; and his flight review is valid until the end of [the month]. The aircraft was fresh from annual and was properly signed off in maintenance log. [Pilot] was alert and coherent. Admittedly; I was semi-awestruck by his status and flying experience. I told him I was not going to charge him for the flight review as I thought it was an honor for me. Take off was normal; although it was gusty with thunderstorms forecast for late afternoon. I was a little uncomfortable with the aircraft age (1950's) although it is immaculate; well maintained and had many recent avionics upgrades. I lack experience and familiarity with this aircraft. It has lap belts only and a throw-over yoke which he familiarized me with. I internally questioned if I would have the presence of mind to bring the yoke to my side safely in an emergency. Also the layout of the panel and associated controls was unfamiliar to me. Additionally; this was my first time at this landing strip; a grass strip with wires and trees in proximity. As we flew we noticed the stall warning horn was not functioning. He said he had the stall horn and gear 'serviced' at the last annual and was disappointed that it was not working. He did not elaborate and I have limited knowledge of the finer points of this aircraft systems. At no time did I handle controls; manipulate any systems or communicate on the radio. I also was having intermittent issues with my headset connection during the flight. It seemed like a poor connection. As we approached the field to land the wind was a gusty left crosswind at about 15 kts. There is a power line on the approach end of the runway with one wire section underground closest to the approach path. An adjacent property had a large [gathering of people]. I distinctly recall having to move my left leg so the pilot could lower the gear. I was focused on the power line and the crosswind and don't recall if there were 3 green lights on gear position. It was gusty and I knew that with the throw over yoke; I was just a passenger and I don't like that feeling as I am a control freak. The plane seemed close to the ground and then the prop kicked up dirt; the pilot yelled 'the gear didn't go down '. We slid on the grass strip and came to rest upright. He secured the power and we exited the plane. Neither of us were injured and nothing on the ground was contacted. No leaks from the aircraft were noted. I looked in the cockpit and noted the gear selector was in the down position. The prop was bent on both tips. The pilot's neighbors showed up quickly and a piece of heavy equipment was used with straps to lift the plane up. The main gear was extended and the nose doors were bent; but manually pulled open and the nose gear was extended and locked. I am not an A&P but I did not even see much scratching of the under belly of the aircraft. Other than the dents on nose wheel gear doors; the rolled prop tips; and some antennas dislodged from the belly; I did not see and he did not mention any other damage. The plane was towed back to the hangar with a golf cart. The pilot was upset and not in a good mood after the incident. I felt like crap about the entire event. I don't see me flying again in a general aircraft where I don't have controls available to me all the time. It would not have prevented this most likely; but I would not be worried about what happen if I needed to take controls.