Carlos Alejo is right, but I wanted to add a few grammatical explanations.
The verb terminar can be intransitive ("to finish"), or transitive ("to finish off sth", "to terminate sth"). The verb terminarse has the same meanings, plus the sense of "to run out". That means the two sentences below are equivalent:
El partido está a punto de terminar = El partido está a punto de terminarse.
because the sense of "finishing" is present in both terminar and terminarse. However, to say "we ran out of cookies" you can only say:
Las galletas se terminaron
and not ٭las galletas terminaron because the sense of "running out" is only present in terminarse.
The pronoun se in terminarse can be analysed in different ways: when it means "to finish" it can be considered an ethic dative; when it means "to run out of" it is a pronominal verb marker (marca de verbo pronominal). Ethic datives don't change the meaning of a verb and can be dropped (that's why the first two sentences are equivalent), while pronominal verbs markers can't be dropped. Sometimes, dropping a pronominal verb marker changes the meaning of a verb, as in acordar ("agree to") and acordarse ("remember"); and sometimes, dropping it leaves you with a verb that doesn't mean anything, as in enterarse ("find out"), whose non-pronominal form, enterar, just doesn't exist. [EDIT: Enterarse isn't a great example because the non-pronominal form, albeit less common, also exists and it means "to inform". Dignarse, arrepentirse or atenerse are better examples.]
I guess "ethic dative" and "pronominal verb marker" are two cases you have to add to your list.