The concept is hits people right in the feels with Fry's loyal and loving mutt Seymour taking the place of the Godfather's kitty. Therefore, with Fry taking the place of the Godfather one can't help but chuckle and want to cry at the same time. For anyone that hasn't seen the referenced Futurama Episode, check out the episode entitled Jurassic Bark. The dyslexic use of the word Dog rather than God works great too on another comedic level.
As for the artwork. It's tight. Firstly, the almost black and white tone is a perfect tribute for the Godfather's original image (shown above). The shading, the highlights, all top notch. Secondly, the seriously expressions and tone given to Fry is hilarious in its own right. But as mentioned earlier, the design elements bring a slew of mixed emotions making it bittersweet. Considering that Fry's character is more of the Slapstick type, this is a feat in and of itself. Thirdly, Having the dog's tongue stick out as bright Red really adds emphasis to Seymour and his emotion. Almost animating the t-shirt. Finally, it is as if Matt Groening and crew designed this themselves. They were always masterfully pulling on the audience's heart strings. This design is that good in terms of art and concept. A great tee for anyone who likes the dog that waited, especially.