Hi Brit, Thanks for these objections. My responses are in brackets.

OK, point taken.  But I am less certain about the tenure process.  We
strive for tenure because, according to arbitrary rules of the
profession ("Publish 6 articles in the course of 6 years in a
tenure-track position"), it is success.  Even if tenure is not
/actually/ performed for the recreation of participants or spectators,
or to sharpen skills, it could be (typically) performed for these
reasons.  But the tenure process is not a game.

[As we agree that we don’t seek tenure because we value the pursuit, but so as not to perish,
to get higher pay, job security, we agree it isn’t (on my account anyhow) a game.
I don’t think, to defend my thesis, I
must argue that seeking tenure couldn’t be a game.  Also the department’s telling me
what level of scholarly success is required for it to support my tenure, what is expected of me to get its support,
doesn’t seem a rule, and, even if it is a rule, it  doesn’t define or create tenure, which is awarded not by the department but by the university, which may deny tenure despite the department’s recommendation. ]

Or consider greetings.  We shake hands because an arbitrary rule says
that a handshake in certain circumstances is a successful greeting,
not because shaking hands is intrinsically valuable.  Shaking hands
probably is not typically performed for the recreation of participants
or spectators but greeting ceremonies around the world might be.  Yet
they are not games.

[Again, we agree that folks typically don’t shake hands (or use other customary greetings) for the recreation of participants or spectators or to sharpen skills, so we agree that, on my account anyhow, such greetings aren’t games. And so it goes around the world. I don’t think that, to defend my account, I must show that non-games couldn’t under any circumstances, be games.]

Many celebrations will satisfy your definition of a game.  Or so it
seems to me. Christmas celebrations involve customs such as bringing
evergreens inside in December, dancing around them, eating herring and
fatty foods, drinking caraway snaps.  These customs are typically
performed for the recreation of participants or spectators, and we
seek the goal of Christmas celebrations because an arbitrary rule says
that performing these customs is success, not because they are
intrinsically valuable.    

[I don’t see customs as typically rules, but set that aside. I wrote:

‘Notice that checkmate isn't success because we strive for it; rather, we strive for checkmate because, according to the rules, it is success. Games have the feature that the success state is in this way internal to the rules. The immediate object of a game is to accomplish the state the rules define as success because it is so defined.’

The customs you mention are meant to set the stage for having fun and good cheer, it’s a kind of party. The success of such a celebration is a matter of people having a good time, and it is pursued because having a good time is intrinsically valuable (we just want to have fun), not because a rule states that having a good time is success.

Even if there are rules for setting the stage for such a party (we bring in a tree, etc) we typically do not follow them because we enjoy setting up the party but because a well staged party has instrumental value–it increases the prospects that people will enjoy themselves. If no one was going to attend we wouldn’t do it.]

Thanks again, Jim