Game progression mechanics (mechanics to progress the player through the game)
Performance mechanics / Rewards and skills mastery mechanics (mechanics to encourage the player to improve and extend their range of skills and judgement)
Narrative mechanics (tools to progress /unfold or bring together one or more apparent story threads in relation to game play). Are dramatic mechanics a subset?
Behavioural & Role assimilation mechanics (mechanics become habit through repeated gameplay, accustomed to see things in certain ways)
Insight and reversal mechanics (mechanics that disrupt the in-game or real-world expectations and presumptions of the player acquired previously or during the game in order to reveal to them a viewpoint taken for granted, or to supplant the view created by gameplay but a view the designer wants them to suddenly by alienated from).