Posts on Sidebar only

Looks like the site you mentioned used a Text Widget.
Did you try to add a new image to the media library and then add a text widget on your sidebar?
Just copy the full path of the image you uploaded and then add a link surrounding the image.

Steps:

  • Add an image in the Media Library.
  • Copy the full path of the uploaded image.
  • Go to Appearance > Widgets.
  • Add a Text Widget to the sidebar.
  • Type a title and then add an img HTML tag with the URL you copied previously.
  • Add a anchor tag around the img tag.
  • Save the changes.

Hope it helps.

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