Yay game designers! Hello!
I'm familiar with the Forge theories and all and really love them, though this addition of Toy sounds more like Koster's work.

Lemme just point out, this analysis is missing the key connection: play, as in rolePlay :P and now I intend to ramble on this topic, hopefully catching on some discussion :D

Edwards (GNS) was all about roleplay, and hence, in the strict activity genre, the theory was (ok, arguably, but whatever) complete. Putting the Toy in, opens up a whole lot of areas besides game design. And we're not talking about "dice in roleplay" as toys (that bit opened my eyes for rpg design when I first stumbled upon it).

The point is that you can apparently do a lot with play:

• play --> a game (football)
• play --> with a toy (ball)
• simulation <-- plays out (football manager)
• narrative <-- plays out (story of a footballer)

The first two are active (play --> what), and last two are passive (what <-- plays). This can be translated to roleplay as: gamist is active (what can we, the players, do in this game), while simulationist and narrativist aim to maintain the entity which provides the joy (story or simulation).

However, simulation and narrative contain games and toys (football manager contains stories of footballers, even if not explicit, which contain game of football which contains ball), therefore they are a higher order of complexity. That's why Edwards used the word Gamist, instead of Game, as he was talking about the focus of the game/-/play.

A toy is an object with which you can play. Game is a system (of rules) with / which you can play. What's the distinction? Physicality of the toy? Meh.

Furthermore, having connected "Choose your own adventure books", "computer games", and "tabletop roleplay", this opens many many many other areas:

• play an instrument
• play with yourself ^^
• play someone (game someone?), as in cheat, rob, or make fun of someone (turn them into a toy)
• play with a quarterly tax report (as in fiddle; regardless of the definitions of play necessarily being non-practical)
• or play in a play (act), for that matter

So, musical instruments are toys, music is a system of rules, and a particular music piece is a narrative that plays out? That's like 99.99% correct, and the 0.01% is killing me :D

In conclusion, many many many distinctions can be made on the level you describe. So many in fact that they easily cease to be useful, even for game design. Equally important as their distinctions is their connection, for the understanding of many facets of the verb play is what generates these distinctions in the first place.

Play is however elusive, often indescribable. Yeah there are definitions, often seriously faulty though, but what they always fail is to grasp play, and this is precisely for the reason there are many many facets to it. If you let in Toy in the distinction, you have opened up floodgates of numerous activities and mental stances.

It seems to me thus that the play is most easily observed on its distinctions, its facets; however, the point of those distinctions in analysis should thus never be to distinguish for their own sake, but to explain their connection, what creates them, because the first (distinguishing) is futile and misleading (floodgates are open), and the second deep, but unfathomable.

Cheers, hope I brought something worth pondering over :)

p.s. Something completely different :)
Here's a little something from guru Osho, who might have a lousy character, but still, this is a very interesting passage on the topic of goals (games vs play):

The question he was asked was:

You have said that there are no goals in life, no purpose. And yet we are all here with enlightenment as our goal. Please speak on this.