Those are your rivers. They're short because the height map is a lot of little pits all over the place.
Filter>>Fill>>Fill Basins should fill all of those little pits and let you get your rivers longer as shown in attachment 1.
If you offset the sea areas below water level before doing the flow finding operation then you'll get the rivers just on land. In the case of the map you showed, the canyons are also below sea level, which will shorten the rivers a bit. If you select everything above sea level using Select>>From Terrain>>Height Range you'll have the canyons in the water, but Select>>Modify>>Expand:1 followed by Select>>Modify>>Contract:1 will fill in single pixel-wide things like the canyons. Attachment 2 shows these results.
One of these years I might get around to doing river width and antialiasing, but I'm a little swamped with other things at the moment.