I don't think that's a meaningful distinction. In a purely technical sense, sure, not half of the human beings alive at the time voted for one candidate. That has never happened and will likely never happen in the US.
But in common parlance, it is acceptable to say that half the country voted for one or another candidate. It happens all the time:
Just because it's common parlance does not mean it's a good practice. HN is supposed to be a forum for reasoned discussion. Any kind of sophistry or propaganda should be called out. Since Trump describes his regime as having an "unprecedented and powerful mandate", and this is actually incorrect in several ways, it is worth drawing the distinction here.
Another way in which Trump is incorrect is that his election victory margin is average among presidential elections in terms of both electoral vote margin and popular vote margin.
I only see the hill article using that parlance. I looked at the articles the hill certainly says half the country voted for Trump. It is an opinion piece you linked to though not a news piece.
The center for politics and global citizen articles do not seem to use half that way though.
For center for politics the title starts with "How the Other Half Votes" and they seem to keep to that usage and never use half of USA/America.
For Global Citizen the title starts with "Half the Planet Will Vote This Year" an they seem to stick to that and never use half of USA/America
I intentionally linked to variations on that wording to show there's a pattern. If you're looking for those exact words, you can find plenty more examples online.
I do not see the pattern you are seeing. What I would need to change my mind here are communities using the parlance correctly, understanding the meaning, and it not leading to misunderstandings to a reasonable percent of the community.
But in common parlance, it is acceptable to say that half the country voted for one or another candidate. It happens all the time:
https://thehill.com/opinion/4935813-trump-appeal-conservatis...
https://centerforpolitics.org/crystalball/how-the-other-half...
https://www.globalcitizen.org/en/content/voting-elections-de...