In the first section of the article:
> While the emperor holds no political power, he serves as a national figurehead.
> While the emperor holds no political power, he serves as a national figurehead.
This is rather different compared to the constitutional monarchies that are common in Europe: it's hard to imagine any major political party (even the hard-right parties) arguing against the monarch if the monarch is suggesting a more liberal position.
For some history, this is the second time Abe has been prime minister. The first time he had to resign. This was directly after proposing the constitutional change. Now, Wikipedia (and the western media it seems) reported that Abe resigned due to the poor performance of his economic policies. However, at the time my impression was that he resigned over the backlash to the constitutional proposals. At the time my Japanese wasn't very good, so I could definitely have gotten it wrong, but that was certainly what I understood.
Fast forward to a few years ago. Abe got back into power, instituted his Abenomics and then re-proposed the constitutional changes. It seemed like it was inevitable because they had enough time to push through the changes and write the constitutional law before the next general election. And then out of the blue the emperor announced, "I want to retire. Please implement the constitutional changes that would allow me to do so". These changes, perhaps not incidentally, meant that Abe could not draft his changes until after the next general election.
It has been suggested (by the NHK no less -- unfortunately you'll have to take my word for it, but that's where I heard of the notion) that this was an intentional move by the emperor. Who knows... However it is true that he has been suffering from poor health and has not been able to perform all of his duties.
Anyway, the general election was held and Abe and the LDP survived, so presumably they will go ahead with their plans. However, the latest I've seen is that there is still considerable opposition in the populace (with over 50% of the population opposing any changes to the constitution). The last I heard Abe has said that he might not go forward with it.
They are under increasing pressure from the US, though. Also, Japan has wanted the US out of Okinawa for a long time, with the US always promising that they will leave as soon as their base in Guam is complete (which never seems to happen). I don't think the US will ever leave Okinawa without Japan being able to take military action the in the sea of Japan because otherwise China will pretty much have free reign there. At the moment, all Japan can do is show up with the coast guard and say "Please leave. Pretty please".
A curious point.
(This led to a small group of retired emperors, called the 'cloistered emperors', who were nominally Buddhist monks and ordinary citizens but in fact did much of the actual work of ruling the country, since the actual emperor was too busy with religious duties to exert much political power)
The system in my country is that until you take the throne you get a relatively normal life. Hell doesn't start until you're at least 40. The Royal family has 400 years of experience so they're used to it. Relatively few ran away or killed themselves. Although a few did go nuts. They know it has to be done.