It's not that monospace fonts have characters that aren't monospaced, is that very few of them have the necessary characters. When a character is missing, the OS will use an alternate font for that character.
For example, the "Courier New" on this machine doesn't have any of the "BOX DRAWINGS HEAVY" characters (such as U+250F, BOX DRAWINGS HEAVY DOWN AND RIGHT, ┏), only "BOX DRAWINGS LIGHT" characters (such as U+250C, BOX DRAWINGS LIGHT DOWN AND RIGHT, ┌).
You used characters not present in my "Courier New", including "BOX DRAWINGS HEAVY DOWN AND RIGHT". Those characters are being fetched from another font, perhaps Arial, causing the diagram to be distorted.
Had you used only characters present in my "Courier New", such as "BOX DRAWINGS LIGHT DOWN AND RIGHT", the diagram would not be distorted.
So yes, totally a font issue, though not quite the one you described.