I lean towards agreeing with you that a simple website plus cheap laptop would the real world best case, but I can understand why you would want a native app.
I agree a web app isn't great for low friction data entry, but they only enter the totals for each candidate x each round, so that'd be a dozen or two dozen short numbers for the whole night per user.
I found this which has some specifics: https://www.cnn.com/2020/02/04/politics/iowa-caucus-voting-a...
The only extra thing I see is a photo upload. Which is not rocket science from a web app either. At least on iOS you can take people right to the photo gallery or the camera.
I would really like to believe this isn't a flask app I couldn't whip up in an afternoon and polish over a week in my free time... but I'm having a hard time.
Working in the depths of google and running a company are two very different things.
My personal experience with google engineers is 20% code and 80% complaining that our issue tracking system isn't as perfect as googles was.