In an amusing note, a River is defined as more than one water stone in a line.
A straight line of Water Stones (more than one) is called a River. (pg. 6, para. 2)
The next line says a river moves when a water stone is placed next to a river.
If a Water Stone is placed orthogonally next to a River, then that River moves ..." (pg. 6, para 2)
Using substitution, this line should read: "If a Water Stone is placed orthogonally next to a straight line of (more than one) water stones, then that river moves ..."
Thus a water stone placed next to one stone would not move. A water stone placed next to more than one stone would move.
Of course this is not the intention as Example B disagrees with this interpretation.