Right now there is a German couple flying in an autogyro around the world. They are in Australia already, so the Irish guy needs to fly a bit faster if he wants to be the first to round the earth in an autogyro.
Personally, I like the Irish approach better as the Germans made quite a lot of fuzz about their trip:
Round-the-World Trip - Worldflight - Round-the-world trip with a Gyroplane