Trademarks are very much like patents in that sometimes they are aimed at getting rights to things that are a bit out there. Nintendo is apparently trying to trademark a pop-culture phrase that just about everyone will recognize. The company has filed for a trademark with the USPTO for the phrase "On like Donkey Kong."
That is a bit like a maker of foam fingers trying to trademark the phrase "pull my finger." The big monkey surfaced in arcade games back in 1981 and since then there have been several different games with Donkey Kong. The "On Like Donkey Kong" phrase is typically used for all sorts of reasons, none of them having to do with the game.
Nintendo wrote in a statement about the filing, "[On like Donkey Kong] is an old, popular Nintendo phrase that has a number of possible interpretations depending on how it's used. In addition to Nintendo's use, it has been used in popular music, television and film over the years, pointing to Donkey Kong's status as an enduring pop-culture icon and video game superstar." I will be surprised if this phrase if given a trademark considering how generic it has become.