There's nothing wrong with the rivers. They all come from mountain ranges or hill regions. Some lead into lakes with outgoing rivers dropping to lower elevations. My assumption is the rivers in the center area are draining towards the sea which is east off the map.
The lake in the top left center edge might be misleading you into thinking the sea viewed on the northwest side is the same thing. I'm assuming the water body at the top left center edge is actually a lake at a fairly high elevation.
If my assumptions are correct - these rivers do not branch unrealistically, IMO.