How did it came about that we do not call Japan an Empire today even though its current head of state Akihito is still officially referred to as "Emperor"?

I will speak in very broad generalizations here.

Japan was a very famous, literal empire in the '40s, and after their capitulation in WWII, their empire was dismantled, both their territorial holdings, and most of the functioning government. The emperor was not dethroned, for political reasons. That's why Japan has an emperor "left over" so to speak.

"Empire" is a vaguely defined word that comes with serious baggage. The big problem is that most emperors and kings of the world aren't actually called "emperor" or "king", these are translations of foreign titles of foreign institutions. But they're translations of convenience, kings are monarchs that rule big lands, emperors rule even bigger lands.

However, Western concept of the emperor is fairly cohesive. We draw our definition from the Roman emperors, who were the martial and administrative nuclei of the overwhelmingly powerful Roman Empire (For the most part). But because the formative years of mass politics were in the 19th and 20th centuries, we also associate the word empire with the vast, powerful, wildly expansionist powers of that era (Who were mostly ruled by emperors using that title to evoke Roman magnificence)

Now back to Japan. Japan has had a figure that we call emperor since at least 500 AD (The earliest emperors are sketchily recorded). While the Roman emperors were below gods and politically dominant, the emperors of Japan were heads of the Shinto faith, and for quite a long time merely figureheads for *shoguns. The Japanese word for the Emperor of Japan is *tenno

Quite obviously, these offices aren't the same. But in the 19th century, a Japanese state became a vast, powerful, expansionist power. It's head of state was the *tenno, who Westerners then called emperor.

Why are there no more empires in the West? Most of the Western emperors had their empires dismantled, or were replaced by republicans (any non-monarchical governments).

The British monarch is a secular, apolitical office, and its imperial title was 'Emperor/Empress of India". When India became independent in '48, they lost that title. No more emperor, and with decolonisation, no imperium to rule.

The Russian monarch was a semi-religious title with absolutist political power, but the last Emperor was overthrown in violence. The Russian Revolution was organised around explicitly deposing the Emperor of Russia to be replaced by a People's Government, and they succeeded. The great imperium gained by Tsarist Russia was mostly still controlled by Russians though.

The Japanese monarch is a religious title, with constitutional powers. After WWII the secular governing body of Japan was deposed, and the remaining political power of the emperor was removed. But the US occupying force did not want to depose the emperor, because they believed the Japanese would not accept a foreign power abolishing their Religious leader. The *tenno remained.

Finally, it should be said the empires and imperialism do not require emperors. With Britain and Japan, for example, the administrators and governors of their empire was not actually the emperor themselves. You've probably heard of people referring to an "American empire", or a "business empire", and these phrases are simply meant to evoke a powerful institution with a heavily centralized nucleus of power. They do not require literal emperors.

Basically, an empire is as much a construct of our thinking as it is an actual title. Japan today does not act like an "empire", so we don't call it that. The Emperor of Japan was not the same as a Western emperor, we just translate *tenno as emperor.