This is a method of propelling a boat, a little like punting, in that one stands, but instead of a punt, a single oar is used: The oar is rested on the stern, and figure of eight movements are made with the oar. Is there a word for this?

sculling

http://www.glen-l.com/designs/special/scullboat.html

Can't tell you what it is, but I can tell you it is not sculling.

Leaving near Philadelphia, there is rowing and sculling on almost every available body of water, and the participants are sitting down.

The method you describe brings to mind the method of gondoliers.

Here's some info I googled:

" In some parts of the world, rowing facing forwards is the prevailing style. The gondolas of Venice are a good example. They are rowed facing forward, standing up, and pushing on a single oar. The boats have developed to suit that style. Gondolas are stable enough to stand up in and their hulls are shaped with a sideways curve (like a banana) to compensate for the one-sided power application. Asian river men row their boats facing forward. Some people "scull" their boats using a single oar off the transom, waging it back and for forth like a fish's tail."

http://www.frontrower.com/whywerowbackward.htm

Quote:

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Asian river men row their boats facing forward. Some people "scull" their boats using a single oar off the transom, waging it back and for forth like a fish's tail.

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That's it. The-standy-uppy-single-oared-figure-of-eighting-boat-propulsion-technique.