The picture is of John Wick, a character known for fighting an entire criminal underground because someone killed his puppy.
Kristi Noem is the governor of South Dakota. She wrote a book detailing how she went hunting with a puppy, the puppy scared birds she was hunting, so she put a bullet into it's head. She admitted it was an untrained puppy so the conclusion many draw is that she needlessly murdered a dog that she could have otherwise trained.
The punchline is that John Wick is coming after her because she killed a puppy.