Yes, glacier melting should mean more water. That is not what the graph labeled "The Rhine river has been receding as alpine glaciers at its source melt" shows.

Another alternative is that, because temperatures are warmer and there is less water stored in the glaciers during winter and less melting in summer, there should be a wider depth variation between winter and summer but a similar average. Also not what the graph shows.

It seems like it is just less precipitation. (Which is climate change, possibly due to global warming)