The reality is, most games are pretty good. I'd say a 7.

The problem with your train of thinking is that it's a review score, not a percentile.  So an average game would be in the 50th percentile or a 5/10.  But reviews are not percentile scores.  They are an evaluation.  If a perfect game is 10/10, average games are not 50% of a perfect game.  Most games are at least somewhat entertaining experiences.  Scores below 50% should indicate that the developers did more wrong than right with a game.  

So, if a 1/10 would be something like "The Letter" on Wii U with virtually no effort, incomplete, poor graphics, etc, and a 10/10 is Breath of the Wild with excellent visuals, sound, content, gameplay, most games would be much closer to Breath than letter.  So if I were evaluating a typical average release these days - like say the latest Assassin's Creed that comes along - I would say it has very good graphics, sound, content, etc.  The gameplay may not be as engrossing as Zelda, and it may not have the uniqueness of the experience, but it would still be a well produced product.  It does more things well than not.  As such, its score should exceed 50%.  As an average, typcial "good" game that comes out each year, it probably scores around 7.5/10.

7.

Comparing it to a middle school grading system right now - A 5/10 would barely be a "positive mark" so to speak.
The class average is most certainly higher, a 7/10 seems like a good bet to me.

I go by the school rating system. A 7 is 70%. 70 is a C-. C is the score of mediocrity. I'd say that is average.

My personal average score is a 7. As far as Metascore goes I'd say 7.5 because a lot of reviewers just love to give high scores indiscriminately.

5 out of 10 for movies and 7.5 out of 10 for games. A 5 out of 10 for a game usual means the game is bad.

I'm picking 6 as average game. If 5 is the middle. Than it's half and half. Both halves cancel each other out. I'd count it as whatever. A 6 and above. You're better than being bad. Just like 65 is passing, for school tests.

If I would rate all games, including free mobile/online games, my average would probably be around 2/10.

But if only 'actual games' count, I think the average should be around 7/10. To me, 7/10 means a decent game, quite all right but not that good (just like the school system).

Well, average is a well-defined term, so technically, I roll with that. I don't know what the average actually is, but I imagine it's around 7, give or take 'a bit'.

On a scale of 1-10, 5-6 would be average (5 would effectively be "average with issues"). 1-5 scale (with none of those cop out percentiles) is way easier; 1 is utter garbage, 3 will scratch that genre itch, 5 is an event, fill in the blanks.