From my perspective as a game designer I can support aspects of MDA from an analysis I did on various definitions of a game. Essentially I came up with something similar: game mechanics, play mechanics and game-play experience. Which I then defined as:
Game mechanics are composed of objects composed of properties. These objects have procedural relationships (rules) with other objects. These objects and their procedures exist in a given time and space which can also exert procedural relationships on the objects.
Play mechanics are about how the player interacts with the game mechanics. This is affected by how the game deals with goals, control and feedback, which are all tweaked to a certain quality, frequency and clarity. This concept reflects things like flow, interesting choices, learning curves, feel, player strategies, etc.
Game-play experience is all about understanding what an experience is. At the core an experience is our mind-body relationship which is essential for how we experience emotion. Next we challenge this relationship by forcing the player to use his/her faculties (eyes, ears, sense of touch, etc.) in different forms of game-play (competition, chance, skill, role-playing, etc.). And as if this wasn't enough... the experience is in constant flux as the player continues to play. These would include: Anticipation, Surprise, Pleasure, Understanding, Strength (Mastery and Empowerment), and Poise (Grace and Composure).
Just a quick rant about how i view the aims of game design these days...