I laughed then thought.

http://gizmodo.com/5526230/cub-scout...deo-game-badge
Read this. Are the scouts coming into modern times, or have they finally given up?

Since it's cub scouts, it's not really a badge that's being offered. It's a pin and a belt loop. Honestly, this isn't too much different than most things you do in cub scouts. Let me list the requirements:

For the Belt Loop:

1. Explain why it is important to have a rating system for video games. Check your video games to be sure they are right for your age.
2. With an adult, create a schedule for you to do things that includes your chores, homework, and video gaming. Do your best to follow this schedule.
3. Learn to play a new video game that is approved by your parent, guardian, or teacher.

For the Pin:

1. With your parents, create a plan to buy a video game that is right for your age group.
2. Compare two game systems (for example, Microsoft Xbox, Sony PlayStation, Nintendo Wii, and so on). Explain some of the differences between the two. List good reasons to purchase or use a game system.
3. Play a video game with family members in a family tournament.
4. Teach an adult or a friend how to play a video game.
5. List at least five tips that would help someone who was learning how to play your favorite video game.
6. Play an appropriate video game with a friend for one hour.
7. Play a video game that will help you practice your math, spelling, or another skill that helps you in your schoolwork.
8. Choose a game you might like to purchase. Compare the price for this game at three different stores. Decide which store has the best deal. In your decision, be sure to consider things like the store return policy and manufacturer’s warranty.
9. With an adult’s supervision, install a gaming system.

Most cub scout activities are based around similar concepts, like this. They involve having the cub plan, teach, and learn, I guess.

/Eagle Scout

Now that that has been answered, I as another question:
Will you're opinion change if:
A: It was a patch,
B: It was for the boy scouts,
C: it was required for either one.

A and B coincide, since it's in Boy Scouts where you begin earning merit badges. I already don't have a very high opinion of the BSA (while my troop was a more liberal than most, the majority of troops are incredibly socially conservative), but I don't think it would necessarily lower my opinion any more. Now, if it became an Eagle required merit badge, then I'd definitely be upset, especially if it replaced one of the 15 already required badges.

Another question:
If any scouting organization gave patches/belt loops/whatever for beating a certain number of video games, would you be upset?

Probably not. Most merit badges don't take that much work to accomplish.