I was discussing with my husband how Redshirt made some of its players uncomfortable for having sexual bigots as NPCs you can't block (I think that's what went on? Also I want to play this game even more now). In real life you can usually block annoying people online, and it usually doesn't impact your social life too much, unless they're people you know in real life. By having harassment as a sometimes unavoidable occurrence, this game was saying that sometimes you have to pay a price for social status, which is being harassed online, and often there's nothing you can do about it (but often IRL there are things you can do about it, from blocking offenders to changing your e-mail address).
Every game has some type of value assumption. In Chess, once the king has been captured, the other pieces are powerless (just like a real monarchy?). In Go, preserving and marking the most territory is the way to win. I know I'm not the first person to notice that game mechanics convey ethical information, but it's still kind of fun to take things apart and look at their assumptions about the world.
Mario: Other animals in the world are hostile. You can defeat them by becoming higher than them. You can only move forward.
Match-3 games: The world is a better place when you group identical objects together. Spending your time grouping these objects is worthwhile.
TinyWings: Even if your dreams are impossible, aspiring to them is still fun.
Many JRPGs: If you come across an insurmountable boss/obstacle, constant practicing will let you beat him eventually.
Most "freemium" games: Time = money
I find that story-based games are more difficult to classify this way. Much of the time, the values of point-and-click adventures rely on what the story is saying and not on the level of mechanics. In some ways, mechanics-based values feel like a deeper way of communicating; it's not just that someone told you that everything in this world would try to kill you, it's that you experienced it that way.