Like Big Sexy said, there is no one true definition of the phrase "Good Game". Everyone can consider any type of game a good game. I'll try marking it not only by each sport, but by age level in particular, because I think there are a lot of different ways of thinking that go into this. Plus the picture makes me reminisce of little league. This is all going about kids growing up with their respective sport. This is longwinded, probably unnecessarily, but oh well.
Age 3 or 4-7
In any sport, this is the age bracket where you are trying to get your legs under you, whether it is hockey, baseball, etc. Your team is not expected to win, unless you get the uber-competitive parent who needs to see their child succeed at everything, and it is the end of the world if they don't. Sorry, tangent. That age bracket is roughly the age where kids learn basic mechanics of the sport they want to play, and by the age of 8 or 9, the expectations of a good game rise. So as long as the kids play hard, and are having fun, I see that as a good game.
Age 8-10
This is where the expectations and emotions rise in little league games. The kids are a little older, a little stronger, and have a better grasp of how to play their respective sport. Parents now want their kids to play harder, expecting them to get that big hit, shot, or goal. The kids are still going out, playing hard, learning from their mistakes, and having fun. As long as I see that, I would consider that a good game still.
Age 11-13
More expectations again, hopefully a lot of hard work from the kids to improve their play. This is where the grasp goes from not just playing hard out there, obviously it is still key, but also playing well and minimizing errors. Seeing how bad kids want to improve and play, showing heart. The score still isn't as big a deal, but it is getting there. Playing with a lot of heart, not giving up on either side, and learning from their mistakes inside the game itself is a good game to me.
Age 14-18
This is the high school level, so there are higher expectations as well, mostly from parents. Coaches expect you to really dial in on the fundamentals, because those are the biggest things when playing sports. There is a common theme with me, playing hard, not giving up. Good games are hard working games, whether high or low scoring.
19 and Above
This is college and the pros, so the expectations are higher without a shadow of a doubt. College you still have room to get the fundamentals down 100%. Those games are always fun to watch, especially in the CWS, because they are playing so damn hard for their school. Two teams going hard just get recognition for their school, and opportunity at the next level. Again, playing hard, minimizing mistakes, it all ties together to me.
Now I'll go through the pros. A good game in the professional ranks for me is a team playing hard, never giving up, and being prideful. It can be a complete blowout, but the losing team can gain more respect from me by continuing to play hard, showing that they don't quit, than a team that goes up by 20 points, 6 runs, 4 goals, whatever the score, and just coasts. They get cocky, and act like they don't have to play hard.
The pros aren't different for me like they are for IC. In football, hockey, baseball, etc, I consider games to be good when they are played hard for the duration. When you have people playing hard, you can get over a mistake and move on faster than if someone is just lacksidasical at the time. In hockey, if you are take a lazy penalty, there is the chance that you just cost your team a goal and possibly a win. Baseball, lazy error can possibly lead to a blown lead, or a big inning for the opposing team. So on for football and basketball. Playing hard for the entire game, whether a close game or a blowout, that is what makes a good game for me.