Tether boats run on water, and were typically tethered to run in a clockwise circle. (in the US, they ran counterclockwise)
Look at the right rear sponson, you can see one of the attachment points for the bridle. There is a second point near the front, which in this pic, you cannot see.

Tether racing is the oldest form of sanctioned racing. It has all but died here in the states, but in Europe it is still a big thing. They even run a steam powered class, with speed, I believe, over 40 mph.

I typed 'tether boats' into msn search, and came up with several sites. Check out one of the european club sites and you can get more details.

For international activities, the best place to start looking is weblinksonline.net

They even have links to some airboat sites listed, even our own member, rcairboat78 is listed.