The reason is commodity. People would rather see the score of a game, and maybe then they might read the review. If the score is glowing, it will validate his opinion to buy it and won't read it; if the score is garbage, it will validate his opinion not to buy it and won't read it. Of course, if he has his mind already set in whether to buy it or not before reading the review, he might only pay attention to one group of them, since they will validate his opinion.
If the review does not have a score or a summary, people will not have that reference and possibly skip the whole thing. Being the Internet, there is no lack of opinion to find elsewhere about anything, including a game.
Another reason is metacritic. Believe it or not, metacritic redirects a lot of traffic to game sites, specially those that are not well known. Some publishers pay attention to metacritic, and they might not even consider you to get review copies if you are not listed there. In order to be included in metacritic, one of the requirements includes having an incremental and easily identifiable quantification of the game, and it had to be easily adapted to a 0-100 gradient. Because of that, most sites include one.
And no, 6.5 is not above average in terms of scores. In term of scores, most sites handle a scale that goes like this: 1s and 2s are reserved for the worst things to get the title of games, broken beyond redemption... after that, the scale starts at 6 all to way to the elusive 10. 6s or 7s are considered mediocre games. If a game is functional (and nothing more), it will rate at 6.