I think it's really just an idea that was in the script but was abandoned during filming.
The implication in the script, and in the scene screencapped above, is that he slips his hands into "gloves" built in to the cape which go rigid and make up the structure of the skeleton of the cape.
This would make the whole deal closer to actual bats wings.
However, in scenes where he actually uses the cape he just seems to grab the edges, from what I can see.
It's a shame, because I think if they had shown that the cape is supported by his extended fingers they could have had some really coll and creepy bat-like poses and movements - with the cape actually moving a lot more like real wings - not when gliding, of course, but for example when he's hanging upside down.