The autogyrois an oddball type of aircraft-they llok like airplanes without wings. Instead of wings, they have horizontal (unpowered) rotor, much like a helicopter.
I understand that they are easier to fly than a helicopter…are they still in use?
I don’t know of any production autogyros certified in the United States, but there are homebuilt kits and plans you can buy if you want to build one yourself.
There are a couple of autogyro kits in production now for hobbyist pilots to flit about with on weekends. See http://www.americanautogyro.com/ as an example.
The aviation industry has pretty well passed them by, like dirigibles. AFAIK there are no factory-produced autogyros anywhere, nor are there any used for anything practical (despite that website’s hopeful copy).
There are only a few companies hoping to bring back autogyros. There was one a couple years ago out in Utah that had gotten to the point of having several working prototypes that they were trying to sell to law enforcement as well as for personal use. Last I heard (about 4 years ago), they were going through some tough layoffs so I am not sure if they are still around.
I just read your link, so I guess they are still at it. I had a friend who use to work for them. Apparently they are a VERY Mormon company. Interesting to go to work in an engineering firm and have no coffee available anywhere,
Here’s a British Company that offers kits, and has a piece by Igor Bensen on development of them.
Really does seem like a lot of fun.
I started my flight training in a Farrington Twinstar gyroplane, which is no longer produced. There are still a few people hanging around that build and fly them as a hobby, but not a whole lot going on on the certified front. Groen Brothers Aviation is the only place I know of that is trying to get a model certified right now.
They have all the diadvantages of helicopters and airplanes. 
The model I flew would do about 75-85 mph on 150hp, but would take off in about 100 feet and land with zero rollout.
LOADS of fun to fly.
BTW, check out the PRA if you’re interested in building/learning to fly one.