Do you think I will have time to do all this in one summer?

I plan on playing through the Halo series(I'm already on Halo 2), Sonic the Hedgehog 1-3 and Sonic Adventures 1-2, a few installments in the Legend of Zelda series, Metroid Prime series, Elder Scrolls III: Morrowind, Final Fantasy 7-10, Super Smash Bros. 4, Kirby Triple Deluxe, Pokémon Fire Red, Injustice, and maybe the Arkham trilogy. If age is a factor, I'm 14. Also, my sister works at a camp near a boardwalk, where I spend a lot of time playing Tekken and other games at the arcade. So do you think I will have enough time to do all of this? We drive down to the boardwalk and that is about 3 hours so I can play the 3ds games then. I also play a lot of Minecraft, and will probably quite a bit of that to. I also am in the Summer Reading Program at the library, so that might take some time away from my goals.

We stay at my cousin's lake house and the have a Super Nintendo, so I will probably play some of that also. So overall do you think I can do this? Is this sound to nerdy or like I have no life?

Maybe you can, but I don't think that's a goal worth working towards. Don't get me wrong, I love video games and I spend a lot of my time on them, but they take a lot of time. I don't know how long most of these games are, but that's still a lot of game time.

Depends in how many hours you plan to play games each day.

The sonic games can be completed in one sitting if you play about 12 hours a day. Sonic games are about 3 to 4 hoes long if you take into account deaths.

Final fantasy games takes about 40 to 100+ hours each depending on how complete you want yo be. Ff7, just fighting the 2 weapons takes about an hour each. If you want the knights of the round master materia on all 3 characters, it'll take about 80 to 90 hours. I spent over 120 hours on ff7 just to have 3 master materia of each materia. 8 took about 70 hours because I wanted all the guardian force so a lot of card playing and restarting if I lose.

Morrowind takes about 100 hours.

Halo games are about 20 hours each, for the average player.