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I like the automatic behavior that can be used with enums, for example:
enum {NONE, START, HEY, HO, LAST};
Then it is easy to loop until LAST, and when a new state (or whatever is represented) is added, the logic adapts.
for (int i = NONE; i < LAST; i++)
{
// Do stuff...
}
Add something...
enum {NONE, START, HEY, WEE, HO, LAST};
The loop adapts...
Using an enum documents the valid choices in a terse manner and allows the compiler to enforce them.
If they are using enum store global constants, like Pi, for example, then I don't know what their goal is.