You must see skin and skeleton at once. If you focus only on skin, you can think about how an experience feels, but not understand why it feels that way or how to improve it. If you focus only on skeleton, you can make a game structure that is beautiful in theory, but potentially horrible in practice. If you can manage to focus on both at once, you can see how it all works while feeling the power of your game's experience at the same time.
When we work, we do it because we are obligated to. We work for food because we are slaves to our bellies. We work to pay the rent because we are slaves to our safety and comfort. Some of this servitude is willing servitude, such as willingness to earn money to care for our families, but it is servitude nonetheless. We are doing it because we have to, not because "we feel like it." The more obligated you are to do something, the more it feels like work. The less obligated you are to do something, the more it feels like play. Stated differently, "It is an invariable principle of all play... that whoever plays, plays freely. Whoever must play cannot play."
By this, he seems to mean "we play because we like to." As trivial as it sounds, this is an important characteristic of play. If we don't like to do it, it probably isn't play.
That is, an activity itself cannot be classified as a "work activity" or "play activity." Instead, what matters is one's attitude about the activity.
Curiously, both sandwich and the sushi roll were invented at about the same time (the eighteenth century), though in very different parts of the world, by table gameplayers who were so obsessed with their games that they needed a way to eat without having to stop the game.