"She wants to play video games."
Translation:Makemake ʻo ia e pāʻani wikiō.
There are indeed many uses of "e" in Hawaiian, and even more uses of "i"!
The text below is based on and adapted from Nā Kai ʻEwalu: Beginning Hawaiian Lessons Makahiki 1, Puke 1:
In Hawaiian the difference between the meanings “like to” and “want to” is shown by using different analula.
I want to sing. -> Makemake au e hīmeni.
I like to sing. OR I "like" singing. -> Makemake au i ka hīmeni.
There are so many uses of "e" in Hawaiian! In this case, I believe it makes the verb that follows it the object of the verb before it. Makemake au i ka pāʻani wikiō. = I like the video game. Makemake au e pāʻani wikiō. = I like to video game. (Though we don't use video gaming as a verb in English so we add the word "play".) At least that's the way that I've understood it.
jdmcowan is right. In this case, "video game" is used as a verb. The "e" between two verbs acts as an infinitive for the compound. For example, "Makemake au e hele" means "I want to go." The infinitive within the compound verb is "to go." He correctly points out that English expression does not normally recognize playing video games as a verb. So although most English speakers would not express it this way, the translation for the prompt is more literally "He wants to video game."