I'm not fully familiar with the medium-editor-insert-plugin, so I'm not sure if this is related to your issue or not. I'll attempt to get more familiar with the code and see if I can understand the root cause.
Based on my experience with working with drag and drop images for the root medium-editor code I found that IE9 does not support the File API:
What this means for medium-editor is that when drop fires after dragging a file into the page, the native event.dataTransfer.files is undefined. For all other browsers supported by medium-editor, this mechanism can be used to grab the dragged file to embed it into the page. Thus, we don't support dragging images into medium-editor for IE9, and we don't currently have a workaround.