On what day is the football game is acceptable in English.
Not sure this is important, but which football are we talking about here?
I don't understand why "aia" (there is) is in these sentences.
Aia marks a location of something in space or time.
Would “ ʻO ka pāʻani Pōpeku ka pōʻahia?” Translate to the same phrase?
In English, we can drop the preposition before a day of the week - The game is on which day? The game is which day? That is not possible in Hawaiian. That preposition still needs to be there. So your version would not work.