It is an identifier. Someone who is looking through that list might not know that it is an disambiguation page from the list. They may link to "Donkey Kong" thinking they are going to the character.
They can still link to Donkey Kong and it will show up as a blue link, only it's a redirect to the disambiguation page instead of a direct link. If anything, it causes more confusion the way it is, as the fact that the disambiguation page has parentheses after the name indicates that there is a seperate "Donkey Kong" page (possibly about the character), but it isn't actually the case. It's misleading in this manner, and there's no advantage (it's pretty clear from the page's contents that it's a disambiguation (it should even have a notice pointing this out), and other pages don't pointlessly tell people what they are in the title; if they did, we would end up with "Category:Games (category containing games)" or "Help:Contents (index of the help pages)").
those are descriptors, not identifiers. Descriptors would be redundant, in this case, as the title and namespace give details on what is the page contents. Identifiers, on the other hand, don't give redundant info. "(game)", "(series)", etc. that isn't already in the page title.

"(disambiguation)" lets people know it is a disambiguation page, something that currently doesn't have a namespace.