I interpret the title to mean that a true achievement is something that is a step towards a better life as determined by each person. Haven't read it yet, but I imagine that the problem it alludes to is how people get trapped in a cycle of escapism -> life gets worse -> escapism. The "false" sense of achievement would be those that make you feel like you've achieved something, when actually your life outside of the game hasn't improved at all.

This isn't to say that true achievements can't come from playing games, but I believe for most people the achievements that come from games are false by this definition.