the utmp.h ACCOUNTING macro is set to 9 on my system.

my question is: what "accounting" is it referring to?

Not sure I understand the question, but accounting is software that records who is using what resources. In the 70's and 80's, a company might have one computer and it was expensive. Accounting was used to distribute the costs to the departments that used it.

See these man pages: acct acctsh acctprc acctcom

The utmp struct (record for utmp) has a field, ut_type. This indicates the kind of information a contains. ut_type can be 10 different values 0 - 9.

The defines in utmp.h simply let you use a meaningful word instead of a not-so-meaningful number to find out what type of utmp record you have read.

#define EMPTY           0         /* null record */
#define RUN_LVL         1         
#define BOOT_TIME       2      /* part of boot */
#define OLD_TIME        3       
#define NEW_TIME        4
#define INIT_PROCESS    5       /* Process spawned by "init" */
#define LOGIN_PROCESS   6       /* A "getty" process waiting for login */
#define USER_PROCESS    7       /* A user process */
#define DEAD_PROCESS    8       
#define ACCOUNTING      9        /* an accounting record */
#define UTMAXTYPE       ACCOUNTING   /* Largest legal value of ut_type */