I have only played the original mario game before (I think it's the original xD)
I played it on the same nintendo as seen on the last photo of your post, my dad bought the nintendo out of nostalgia and we had quite a bit of fun completing the game hundreads of times xD
Yes, Super Mario Bros is an original NES game. Its great to read that both you and your dad enjoyed playing Super Mario Bros together (That flying fish stage is a killer). Nostalgia is the reason for our families purchase of the MINI as well. Super Mario World was released on the Super NES, the system that was built after The NES. Both very fun systems.