I'm not able to read the Mainichi article.
I do know that the concept for shrine that I grew up with (shrines being part of the Spanish religious traditions) is very different to that of a temple (or church) and I had to adjust my perception and understanding of the word when I became familiar with Japan in order to accommodate the way this word 'shrine' is used in relation to Shinto.
A lot of people outside Japan are unable to give Shinto the same respect they give their own monotheist or other monotheist religions so it is routinely called a superstitious belief or cult. Since the word 'shrine' also invokes a place of adoration and devotion rather than one of active worship with a suitably ordained religious leader then I guess it might give people ignorant of Shinto cause to dismiss it as a 'real religion' as it has no churches or temples where 'real worship' is supposed to happen.
Anyway, those are just hastily formed views about why I think the change in name might be being considered. Particularly if one were thinking about how to reposition Shinto in a worldwide context. I can see the sense in the decision.